-8x^2-124x+352=-5x^2-79x-184

Solution for -8x^2-124x+352=-5x^2-79x-184 equation:

Simplifying
-8x2 + -124x + 352 = -5x2 + -79x + -184

Reorder the terms:
352 + -124x + -8x2 = -5x2 + -79x + -184

Reorder the terms:
352 + -124x + -8x2 = -184 + -79x + -5x2

Solving
352 + -124x + -8x2 = -184 + -79x + -5x2

Solving for variable 'x'.

Reorder the terms:
352 + 184 + -124x + 79x + -8x2 + 5x2 = -184 + -79x + -5x2 + 184 + 79x + 5x2

Combine like terms: 352 + 184 = 536
536 + -124x + 79x + -8x2 + 5x2 = -184 + -79x + -5x2 + 184 + 79x + 5x2

Combine like terms: -124x + 79x = -45x
536 + -45x + -8x2 + 5x2 = -184 + -79x + -5x2 + 184 + 79x + 5x2

Combine like terms: -8x2 + 5x2 = -3x2
536 + -45x + -3x2 = -184 + -79x + -5x2 + 184 + 79x + 5x2

Reorder the terms:
536 + -45x + -3x2 = -184 + 184 + -79x + 79x + -5x2 + 5x2

Combine like terms: -184 + 184 = 0
536 + -45x + -3x2 = 0 + -79x + 79x + -5x2 + 5x2
536 + -45x + -3x2 = -79x + 79x + -5x2 + 5x2

Combine like terms: -79x + 79x = 0
536 + -45x + -3x2 = 0 + -5x2 + 5x2
536 + -45x + -3x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
536 + -45x + -3x2 = 0

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

Divide each side by '-3'.
-178.6666667 + 15x + x2 = 0

Move the constant term to the right:

Add '178.6666667' to each side of the equation.
-178.6666667 + 15x + 178.6666667 + x2 = 0 + 178.6666667

Reorder the terms:
-178.6666667 + 178.6666667 + 15x + x2 = 0 + 178.6666667

Combine like terms: -178.6666667 + 178.6666667 = 0.0000000
0.0000000 + 15x + x2 = 0 + 178.6666667
15x + x2 = 0 + 178.6666667

Combine like terms: 0 + 178.6666667 = 178.6666667
15x + x2 = 178.6666667

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 178.6666667 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 178.6666667 + 56.25

Combine like terms: 178.6666667 + 56.25 = 234.9166667
56.25 + 15x + x2 = 234.9166667

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 234.9166667

Calculate the square root of the right side: 15.326991443

Break this problem into two subproblems by setting 
(x + 7.5) equal to 15.326991443 and -15.326991443.

Subproblem 1
x + 7.5 = 15.326991443

Simplifying
x + 7.5 = 15.326991443

Reorder the terms:
7.5 + x = 15.326991443

Solving
7.5 + x = 15.326991443

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 15.326991443 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 15.326991443 + -7.5
x = 15.326991443 + -7.5

Combine like terms: 15.326991443 + -7.5 = 7.826991443
x = 7.826991443

Simplifying
x = 7.826991443

Subproblem 2
x + 7.5 = -15.326991443

Simplifying
x + 7.5 = -15.326991443

Reorder the terms:
7.5 + x = -15.326991443

Solving
7.5 + x = -15.326991443

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -15.326991443 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -15.326991443 + -7.5
x = -15.326991443 + -7.5

Combine like terms: -15.326991443 + -7.5 = -22.826991443
x = -22.826991443

Simplifying
x = -22.826991443

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.826991443, -22.826991443}