8*x^2-20*x-120=0

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Solution for 8*x^2-20*x-120=0 equation: 


Simplifying
8x2 + -20x + -120 = 0

Reorder the terms:
-120 + -20x + 8x2 = 0

Solving
-120 + -20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + -5x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-30 + -5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-30 + -5x + 2x2 = 0

Solving
-30 + -5x + 2x2 = 0

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

Divide each side by '2'.
-15 + -2.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -2.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -2.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2.5x + x2 = 0 + 15
-2.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-2.5x + x2 = 15

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 15 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 15 + 1.5625

Combine like terms: 15 + 1.5625 = 16.5625
1.5625 + -2.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + -1.25) equal to 4.069705149 and -4.069705149.


Subproblem 1
x + -1.25 = 4.069705149

Simplifying
x + -1.25 = 4.069705149

Reorder the terms:
-1.25 + x = 4.069705149

Solving
-1.25 + x = 4.069705149

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 4.069705149 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 4.069705149 + 1.25
x = 4.069705149 + 1.25

Combine like terms: 4.069705149 + 1.25 = 5.319705149
x = 5.319705149

Simplifying
x = 5.319705149


Subproblem 2
x + -1.25 = -4.069705149

Simplifying
x + -1.25 = -4.069705149

Reorder the terms:
-1.25 + x = -4.069705149

Solving
-1.25 + x = -4.069705149

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -4.069705149 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -4.069705149 + 1.25
x = -4.069705149 + 1.25

Combine like terms: -4.069705149 + 1.25 = -2.819705149
x = -2.819705149

Simplifying
x = -2.819705149


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.319705149, -2.819705149}
Solution
x = {5.319705149, -2.819705149}

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