Solve the quadratic equation $3x^2-5x-7=0$

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To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=3$, $b=-5$ and $c=-7$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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$x=\frac{5\pm \sqrt{{\left(-5\right)}^2-4\cdot 3\cdot -7}}{2\cdot 3}$

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Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 3x^2-5x+-7=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=3, b=-5 and c=-7. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. Simplifying. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Subtract the values 5 and -10.440307.

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Main Topic: Quadratic Equations

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.

Used Formulas

1. See formulas

Related Topics

  • Quadratic Equations
  • Quadratic Formula

solve the quadratic equation 3x^2 5x 7=0

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Quadratic Equation Solver

We can help you solve an equation of the form " ax 2 + bx + c = 0 " Just enter the values of a, b and c below :

Is it Quadratic?

Only if it can be put in the form ax 2 + bx + c = 0 , and a is not zero .

The name comes from "quad" meaning square, as the variable is squared (in other words x 2 ).

These are all quadratic equations in disguise:

How Does this Work?

The solution(s) to a quadratic equation can be calculated using the Quadratic Formula :

The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !

The blue part ( b 2 - 4ac ) is called the "discriminant", because it can "discriminate" between the possible types of answer:

  • when it is positive, we get two real solutions,
  • when it is zero we get just ONE solution,
  • when it is negative we get complex solutions.

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solve the quadratic equation 3x^2 5x 7=0

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solve the quadratic equation 3x^2 5x 7=0

SOLUTION: Use the quadratic formula to solve the equation. 3x^2-5x-7=0

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Solution - Quadratic equations

Other Ways to Solve

  • Solving quadratic equations by factoring
  • Solving quadratic equations using the quadratic formula
  • Solving quadratic equations by completing the square

Step by Step Solution

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :                       3*x^2-5*x-7-(1)=0 

Step by step solution :

Step  1  :, equation at the end of step  1  :, step  2  :, trying to factor by splitting the middle term.

  2.1       Factoring  3x 2 -5x-8   The first term is,   3x 2   its coefficient is   3   . The middle term is,   -5x   its coefficient is   -5   . The last term, "the constant", is   -8   Step-1 : Multiply the coefficient of the first term by the constant   3  •  -8  = -24   Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is     -5   .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3                        3x 2 - 8x  +  3x - 8 Step-4 : Add up the first 2 terms, pulling out like factors :                      x • (3x-8)               Add up the last 2 terms, pulling out common factors :                      1 •  (3x-8) Step-5 : Add up the four terms of step 4 :                      (x+1)  •  (3x-8)              Which is the desired factorization

Equation at the end of step  2  :

Step  3  :, theory - roots of a product :.

  3.1      A product of several terms equals zero.     When a product of two or more terms equals zero, then at least one of the terms must be zero.     We shall now solve each term = 0 separately     In other words, we are going to solve as many equations as there are terms in the product     Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

  3.2        Solve  :     3x-8 = 0     Add  8   to both sides of the equation :                           3x = 8 Divide both sides of the equation by 3:                       x = 8/3 = 2.667

  3.3        Solve  :     x+1 = 0     Subtract  1   from both sides of the equation :                           x = -1

Supplement : Solving Quadratic Equation Directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex :

  4.1        Find the Vertex of    y = 3x 2 -5x-8 Parabolas have a highest or a lowest point called the Vertex  .    Our parabola opens up and accordingly has a lowest point (AKA absolute minimum)  .    We know this even before plotting  "y"  because the coefficient of the first term,  3  , is positive (greater than zero).     Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x  -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.     Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.     For any parabola, Ax 2 +Bx+C, the  x  -coordinate of the vertex is given by  -B/(2A)  . In our case the  x  coordinate is   0.8333      Plugging into the parabola formula   0.8333  for  x  we can calculate the  y  -coordinate :      y = 3.0 * 0.83 * 0.83 - 5.0 * 0.83 - 8.0 or   y = -10.083

Parabola, Graphing Vertex and X-Intercepts :

Solve quadratic equation by completing the square.

  4.2       Solving    3x 2 -5x-8 = 0 by Completing The Square  .   Divide both sides of the equation by   3  to have 1 as the coefficient of the first term :     x 2 -(5/3)x-(8/3) = 0 Add   8/3   to both side of the equation :     x 2 -(5/3)x = 8/3 Now the clever bit: Take the coefficient of  x  , which is   5/3  , divide by two, giving   5/6  , and finally square it giving   25/36   Add   25/36   to both sides of the equation :   On the right hand side we have :     8/3   +   25/36    The common denominator of the two fractions is  36    Adding  (96/36)+(25/36)  gives  121/36    So adding to both sides we finally get :     x 2 -(5/3)x+(25/36) = 121/36 Adding   25/36   has completed the left hand side into a perfect square :      x 2 -(5/3)x+(25/36)    =     (x-(5/6))  •  (x-(5/6))   =    (x-(5/6)) 2 Things which are equal to the same thing are also equal to one another. Since     x 2 -(5/3)x+(25/36) = 121/36 and     x 2 -(5/3)x+(25/36) = (x-(5/6)) 2 then, according to the law of transitivity,     (x-(5/6)) 2 = 121/36 We'll refer to this Equation as  Eq. #4.2.1   The Square Root Principle says that When two things are equal, their square roots are equal. Note that the square root of      (x-(5/6)) 2   is      (x-(5/6)) 2/2  =    (x-(5/6)) 1  =     x-(5/6) Now, applying the Square Root Principle to   Eq. #4.2.1   we get:      x-(5/6)  = √ 121/36 Add   5/6   to both sides to obtain:     x = 5/6 + √ 121/36 Since a square root has two values, one positive and the other negative     x 2 - (5/3)x - (8/3) = 0    has two solutions:    x = 5/6 + √ 121/36    or    x = 5/6 - √ 121/36 Note that  √ 121/36 can be written as    √  121  / √  36    which is 11 / 6

Solve Quadratic Equation using the Quadratic Formula

  4.3       Solving     3x 2 -5x-8 = 0 by the Quadratic Formula  .   According to the Quadratic Formula,   x   , the solution for    Ax 2 +Bx+C   = 0   , where  A, B   and  C  are numbers, often called coefficients, is given by :                                                    - B  ±  √ B 2 -4AC   x =   ————————                       2A   In our case,   A   =     3                       B   =    -5                       C   =   -8 Accordingly,   B 2   -  4AC   =                      25 - (-96) =                      121 Applying the quadratic formula :                 5 ± √ 121    x  =    —————                     6 Can  √ 121 be simplified ? Yes !    The prime factorization of  121    is      11•11   To be able to remove something from under the radical, there have to be   2   instances of it (because we are taking a square i.e. second root). √ 121   =  √   11•11   =                 ±   11 • √ 1   =                 ±  11 So now we are looking at:             x  =  ( 5 ± 11) / 6 Two real solutions: x =(5+√ 121 )/6=(5+11)/6= 2.667 or: x =(5-√ 121 )/6=(5-11)/6= -1.000

Two solutions were found :

  •  x = -1
  •  x = 8/3 = 2.667

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Terms and topics.

  • Parabola finding vertex and X intercepts
  • Simplifying radicals

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  • Simplifying radicals | Khan Academy
  • Radicals: Introduction & Simplification | Purplemath
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  1. Solve Using the Quadratic Formula 3x^2-5x-7=0

    Algebra Solve Using the Quadratic Formula 3x^2-5x-7=0 3x2 − 5x − 7 = 0 3 x 2 - 5 x - 7 = 0 Use the quadratic formula to find the solutions. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a Substitute the values a = 3 a = 3, b = −5 b = - 5, and c = −7 c = - 7 into the quadratic formula and solve for x x.

  2. Solve 3x^2-5x-7=0

    Steps Using Direct Factoring Method View solution steps Graph Graph Both Sides in 2D Graph in 2D Quiz Quadratic Equation 3x2 −5x−7 = 0 Similar Problems from Web Search 3x2 − 5x − 7 = 0 http://www.tiger-algebra.com/drill/3x~2-5x-7=0/

  3. 3x^2-5x-7=0

    Calculus Functions Linear Algebra Trigonometry Statistics Economics Go Examples Related Symbolab blog posts High School Math Solutions - Quadratic Equations Calculator, Part 2 Solving quadratics by factorizing (link to previous post) usually works just fine. But what if the quadratic equation... Read More Save to Notebook! Sign in Send us Feedback

  4. Quadratic Formula Calculator

    Popular Problems Solve Using the Quadratic Formula x2 +5x+6 = 0 x 2 + 5 x + 6 = 0 Solve Using the Quadratic Formula x2 −9 = 0 x 2 - 9 = 0 Solve Using the Quadratic Formula 5x2 −7x−3 = 0 5 x 2 - 7 x - 3 = 0 Apply the Quadratic Formula x2 −14x+ 49 x 2 - 14 x + 49 Apply the Quadratic Formula x2 −18x− 4 x 2 - 18 x - 4

  5. Solve Quadratic equations 3x^2-5x-7=0 Tiger Algebra Solver

    Step by step solution : Step 1 : Equation at the end of step 1 : (3x2 - 5x) - 7 = 0 Step 2 : Trying to factor by splitting the middle term 2.1 Factoring 3x2-5x-7 The first term is, 3x2 its coefficient is 3 . The middle term is, -5x its coefficient is -5 . The last term, "the constant", is -7

  6. Quadratic Equation Solver

    There are different methods you can use to solve quadratic equations, depending on your particular problem. Solve By Factoring Example: 3x^2-2x-1=0 Complete The Square Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.) Take the Square Root Example: 2x^2=18 Quadratic Formula

  7. Solve 3x^2+5x+7=0

    3x2+5x-+7=0 Two solutions were found : x = (-5-√109)/6=-2.573 x = (-5+√109)/6= 0.907 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 + 5x) - 7 = 0 Step 2 :Trying to ... -x2+5x+7=0 Two solutions were found : x = (-5-√53)/-2= 6.140 x = (-5+√53)/-2=-1.140 Step by step solution : Step 1 :Trying to factor by splitting ...

  8. Solve the quadratic equation 3x^2-5x-7=0 using the Quadratic Formula

    Step-by-step explanation 1. Find the coefficients To find the coefficients, use the standard form of a quadratic equation: a x 2 + b x + c = 0 3 x 2 − 5 x − 7 = 0 a = 3 b = -5 c = -7 2. Plug these coefficients into the quadratic formula To find the roots of a quadratic equation, plug its coefficients ( a, b and c ) into the quadratic formula:

  9. solve the quadratic equation 3x^2-5x-7=0

    answer answered Solve the quadratic equation 3x^2-5x-7=0 Advertisement Answer 21 people found it helpful profile Brainly User 1 Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 . To Find : The roots of the equation . Solution : Given quadratic equation is 3x²-5x-7=0.

  10. Solve Quadratic equations 3x2-5x+7=0 Tiger Algebra Solver

    Step by step solution : Step 1 : Equation at the end of step 1 (3x2 - 5x) + 7 = 0 Step 2 : Trying to factor by splitting the middle term 2.1 Factoring 3x2-5x+7 The first term is, 3x2 its coefficient is 3 . The middle term is, -5x its coefficient is -5 . The last term, "the constant", is +7

  11. Solve the quadratic equation 3x^2-5x+-7=0

    Unlock the first 2 steps of this solution. Learn how to solve problems step by step online. Solve the quadratic equation 3x^2-5x+-7=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=3, b=-5 and c=-7. Then substitute the values of the coefficients of the equation in the quadratic ...

  12. Quadratic Equation Solver

    We can help you solve an equation of the form "ax 2 + bx + c = 0" Just ... square, as the variable is squared (in other words x 2). These are all quadratic equations in disguise: In disguise In standard form a, b and c; x 2 = 3x -1: x 2 - 3x + 1 = 0: a=1, b=-3, c=1: 2(x 2 - 2x) = 5: 2x 2 - 4x - 5 = 0: a=2, b=-4, c=-5: x(x-1) = 3: x 2 - x - 3 ...

  13. Solve 3x^2+5x=7

    3x2+5x=2 Two solutions were found : x = -2 x = 1/3 = 0.333 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ...

  14. Quadratic Formula Calculator

    About the quadratic formula. Solve an equation of the form a x 2 + b x + c = 0 by using the quadratic formula: x =. − b ± √ b 2 − 4 a c. 2 a.

  15. SOLUTION: Use the quadratic formula to solve the equation. 3x^2-5x-7=0

    SOLUTION: Use the quadratic formula to solve the equation. 3x^2-5x-7=0 Quadratics: solvers Practice! Answers archive Lessons Word Problems In Depth Click here to see ALL problems on Quadratic Equations Question 111571: Use the quadratic formula to solve the equation. 3x^2-5x-7=0 Answer by jim_thompson5910 (35256) ( Show Source ):

  16. Solve by Factoring 3x^2-5x-7=0

    Algebra Solve by Factoring 3x^2-5x-7=0 3x2 − 5x − 7 = 0 3 x 2 - 5 x - 7 = 0 Use the quadratic formula to find the solutions. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a Substitute the values a = 3 a = 3, b = −5 b = - 5, and c = −7 c = - 7 into the quadratic formula and solve for x x. 5±√(−5)2 −4 ⋅(3⋅−7) 2⋅3 5 ± ( - 5) 2 - 4 ⋅ ( 3 ⋅ - 7) 2 ⋅ 3

  17. Solve the quadratic equation 3x^2

    Find an answer to your question Solve the quadratic equation 3x^2 - 5x - 7 = 0 Give your answers to 3 significant figures. ... 2.57 or -0.907. Step-by-step explanation: → First state the quadratic formula. → Identify the 'a', 'b' and 'c' variables . a = 3, b = -5 and c = -7.

  18. Solve Using the Quadratic Formula 3x^2+x-5=0

    Popular Problems Algebra Solve Using the Quadratic Formula 3x^2+x-5=0 3x2 + x − 5 = 0 3 x 2 + x - 5 = 0 Use the quadratic formula to find the solutions. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a Substitute the values a = 3 a = 3, b = 1 b = 1, and c = −5 c = - 5 into the quadratic formula and solve for x x.

  19. Solve Quadratic equations -3x^2+5x-7=0 Tiger Algebra Solver

    Tiger shows you, step by step, how to solve YOUR Quadratic Equations -3x^2+5x-7=0 by Completing the Square, Quadratic formula or, whenever possible, by Factoring

  20. Solved Solve the equation 2(3x-4)=5(x+2)-7. Show all your

    Solve the equation 2(3x-4)=5(x+2)-7. Show all your steps in your calculation.Consider the quadratic equation 6x2-x-15=0. Factor the equation completely and solve for x. Show all steps of your work, including how vou determine the factors and the roots of the equation.

  21. Solve Quadratic equations 3x^2-5x-7=1 Tiger Algebra Solver

    Supplement : Solving Quadratic Equation Directly Solving 3x 2-5x-8 = 0 directly . Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula. Parabola, Finding the Vertex : 4.1 Find the Vertex of y = 3x 2-5x-8 Parabolas have a highest or a lowest ...

  22. Quadratic Equation Calculator

    The quadratic formula gives solutions to the quadratic equation ax^2+bx+c=0 and is written in the form of x = (-b ± √(b^2 - 4ac)) / (2a) Does any quadratic equation have two solutions? There can be 0, 1 or 2 solutions to a quadratic equation.

  23. Solve Using the Quadratic Formula 3x^2-5x-2=0

    Popular Problems Algebra Solve Using the Quadratic Formula 3x^2-5x-2=0 3x2 − 5x − 2 = 0 3 x 2 - 5 x - 2 = 0 Use the quadratic formula to find the solutions. −b±√b2 −4(ac) 2a - b ± b 2 - 4 ( a c) 2 a Substitute the values a = 3 a = 3, b = −5 b = - 5, and c = −2 c = - 2 into the quadratic formula and solve for x x.

  24. 3x^2-5x+2=0

    Free quadratic equation calculator - Solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step ... quadratic-equation-calculator. 3x^{2}-5x+2=0. en. Related Symbolab blog posts. High School Math Solutions - Quadratic Equations Calculator, Part 3.