3x^2+14x-120=0

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Solution for 3x^2+14x-120=0 equation: 


Simplifying
3x2 + 14x + -120 = 0

Reorder the terms:
-120 + 14x + 3x2 = 0

Solving
-120 + 14x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-40 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 4.666666667x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 4.666666667x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 4.666666667x + x2 = 0 + 40
4.666666667x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
4.666666667x + x2 = 40

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 40 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 40 + 5.444444448

Combine like terms: 40 + 5.444444448 = 45.444444448
5.444444448 + 4.666666667x + x2 = 45.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 45.444444448

Calculate the square root of the right side: 6.741249472

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 6.741249472 and -6.741249472.


Subproblem 1
x + 2.333333334 = 6.741249472

Simplifying
x + 2.333333334 = 6.741249472

Reorder the terms:
2.333333334 + x = 6.741249472

Solving
2.333333334 + x = 6.741249472

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 6.741249472 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 6.741249472 + -2.333333334
x = 6.741249472 + -2.333333334

Combine like terms: 6.741249472 + -2.333333334 = 4.407916138
x = 4.407916138

Simplifying
x = 4.407916138


Subproblem 2
x + 2.333333334 = -6.741249472

Simplifying
x + 2.333333334 = -6.741249472

Reorder the terms:
2.333333334 + x = -6.741249472

Solving
2.333333334 + x = -6.741249472

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -6.741249472 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -6.741249472 + -2.333333334
x = -6.741249472 + -2.333333334

Combine like terms: -6.741249472 + -2.333333334 = -9.074582806
x = -9.074582806

Simplifying
x = -9.074582806


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.407916138, -9.074582806}

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