8x^2+26x-6=0

Solution for 8x^2+26x-6=0 equation:

Simplifying
8x2 + 26x + -6 = 0

Reorder the terms:
-6 + 26x + 8x2 = 0

Solving
-6 + 26x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 13x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 13x + 4x2)' equal to zero and attempt to solve:

Simplifying
-3 + 13x + 4x2 = 0

Solving
-3 + 13x + 4x2 = 0

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

Divide each side by '4'.
-0.75 + 3.25x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 3.25x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 3.25x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 3.25x + x2 = 0 + 0.75
3.25x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
3.25x + x2 = 0.75

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = 0.75 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 0.75 + 2.640625

Combine like terms: 0.75 + 2.640625 = 3.390625
2.640625 + 3.25x + x2 = 3.390625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(x + 1.625) equal to 1.841364983 and -1.841364983.

Subproblem 1
x + 1.625 = 1.841364983

Simplifying
x + 1.625 = 1.841364983

Reorder the terms:
1.625 + x = 1.841364983

Solving
1.625 + x = 1.841364983

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = 1.841364983 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = 1.841364983 + -1.625
x = 1.841364983 + -1.625

Combine like terms: 1.841364983 + -1.625 = 0.216364983
x = 0.216364983

Simplifying
x = 0.216364983

Subproblem 2
x + 1.625 = -1.841364983

Simplifying
x + 1.625 = -1.841364983

Reorder the terms:
1.625 + x = -1.841364983

Solving
1.625 + x = -1.841364983

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = -1.841364983 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = -1.841364983 + -1.625
x = -1.841364983 + -1.625

Combine like terms: -1.841364983 + -1.625 = -3.466364983
x = -3.466364983

Simplifying
x = -3.466364983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.216364983, -3.466364983}
Solution
x = {0.216364983, -3.466364983}