115.2x^2+8x-90=0

Solution for 115.2x^2+8x-90=0 equation:

Simplifying
115.2x2 + 8x + -90 = 0

Reorder the terms:
-90 + 8x + 115.2x2 = 0

Solving
-90 + 8x + 115.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '115.2'.
-0.78125 + 0.06944444444x + x2 = 0

Move the constant term to the right:

Add '0.78125' to each side of the equation.
-0.78125 + 0.06944444444x + 0.78125 + x2 = 0 + 0.78125

Reorder the terms:
-0.78125 + 0.78125 + 0.06944444444x + x2 = 0 + 0.78125

Combine like terms: -0.78125 + 0.78125 = 0.00000
0.00000 + 0.06944444444x + x2 = 0 + 0.78125
0.06944444444x + x2 = 0 + 0.78125

Combine like terms: 0 + 0.78125 = 0.78125
0.06944444444x + x2 = 0.78125

The x term is 0.06944444444x.  Take half its coefficient (0.03472222222).
Square it (0.001205632716) and add it to both sides.

Add '0.001205632716' to each side of the equation.
0.06944444444x + 0.001205632716 + x2 = 0.78125 + 0.001205632716

Reorder the terms:
0.001205632716 + 0.06944444444x + x2 = 0.78125 + 0.001205632716

Combine like terms: 0.78125 + 0.001205632716 = 0.782455632716
0.001205632716 + 0.06944444444x + x2 = 0.782455632716

Factor a perfect square on the left side:
(x + 0.03472222222)(x + 0.03472222222) = 0.782455632716

Calculate the square root of the right side: 0.884565222

Break this problem into two subproblems by setting 
(x + 0.03472222222) equal to 0.884565222 and -0.884565222.

Subproblem 1
x + 0.03472222222 = 0.884565222

Simplifying
x + 0.03472222222 = 0.884565222

Reorder the terms:
0.03472222222 + x = 0.884565222

Solving
0.03472222222 + x = 0.884565222

Solving for variable 'x'.

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

Add '-0.03472222222' to each side of the equation.
0.03472222222 + -0.03472222222 + x = 0.884565222 + -0.03472222222

Combine like terms: 0.03472222222 + -0.03472222222 = 0.00000000000
0.00000000000 + x = 0.884565222 + -0.03472222222
x = 0.884565222 + -0.03472222222

Combine like terms: 0.884565222 + -0.03472222222 = 0.84984299978
x = 0.84984299978

Simplifying
x = 0.84984299978

Subproblem 2
x + 0.03472222222 = -0.884565222

Simplifying
x + 0.03472222222 = -0.884565222

Reorder the terms:
0.03472222222 + x = -0.884565222

Solving
0.03472222222 + x = -0.884565222

Solving for variable 'x'.

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

Add '-0.03472222222' to each side of the equation.
0.03472222222 + -0.03472222222 + x = -0.884565222 + -0.03472222222

Combine like terms: 0.03472222222 + -0.03472222222 = 0.00000000000
0.00000000000 + x = -0.884565222 + -0.03472222222
x = -0.884565222 + -0.03472222222

Combine like terms: -0.884565222 + -0.03472222222 = -0.91928744422
x = -0.91928744422

Simplifying
x = -0.91928744422

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.84984299978, -0.91928744422}