96x^2+104x-8=0

Solution for 96x^2+104x-8=0 equation:

Simplifying
96x2 + 104x + -8 = 0

Reorder the terms:
-8 + 104x + 96x2 = 0

Solving
-8 + 104x + 96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 13x + 12x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-1 + 13x + 12x2)' equal to zero and attempt to solve:

Simplifying
-1 + 13x + 12x2 = 0

Solving
-1 + 13x + 12x2 = 0

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

Divide each side by '12'.
-0.08333333333 + 1.083333333x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 1.083333333x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 1.083333333x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 1.083333333x + x2 = 0 + 0.08333333333
1.083333333x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
1.083333333x + x2 = 0.08333333333

The x term is 1.083333333x.  Take half its coefficient (0.5416666665).
Square it (0.2934027776) and add it to both sides.

Add '0.2934027776' to each side of the equation.
1.083333333x + 0.2934027776 + x2 = 0.08333333333 + 0.2934027776

Reorder the terms:
0.2934027776 + 1.083333333x + x2 = 0.08333333333 + 0.2934027776

Combine like terms: 0.08333333333 + 0.2934027776 = 0.37673611093
0.2934027776 + 1.083333333x + x2 = 0.37673611093

Factor a perfect square on the left side:
(x + 0.5416666665)(x + 0.5416666665) = 0.37673611093

Calculate the square root of the right side: 0.613788327

Break this problem into two subproblems by setting 
(x + 0.5416666665) equal to 0.613788327 and -0.613788327.

Subproblem 1
x + 0.5416666665 = 0.613788327

Simplifying
x + 0.5416666665 = 0.613788327

Reorder the terms:
0.5416666665 + x = 0.613788327

Solving
0.5416666665 + x = 0.613788327

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = 0.613788327 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = 0.613788327 + -0.5416666665
x = 0.613788327 + -0.5416666665

Combine like terms: 0.613788327 + -0.5416666665 = 0.0721216605
x = 0.0721216605

Simplifying
x = 0.0721216605

Subproblem 2
x + 0.5416666665 = -0.613788327

Simplifying
x + 0.5416666665 = -0.613788327

Reorder the terms:
0.5416666665 + x = -0.613788327

Solving
0.5416666665 + x = -0.613788327

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = -0.613788327 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = -0.613788327 + -0.5416666665
x = -0.613788327 + -0.5416666665

Combine like terms: -0.613788327 + -0.5416666665 = -1.1554549935
x = -1.1554549935

Simplifying
x = -1.1554549935

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0721216605, -1.1554549935}
Solution
x = {0.0721216605, -1.1554549935}