12x^2-26x+8=0

Solution for 12x^2-26x+8=0 equation:

Simplifying
12x2 + -26x + 8 = 0

Reorder the terms:
8 + -26x + 12x2 = 0

Solving
8 + -26x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -13x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -13x + 6x2)' equal to zero and attempt to solve:

Simplifying
4 + -13x + 6x2 = 0

Solving
4 + -13x + 6x2 = 0

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

Divide each side by '6'.
0.6666666667 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2.166666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2.166666667x + x2 = 0 + -0.6666666667
-2.166666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2.166666667x + x2 = -0.6666666667

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = -0.6666666667 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = -0.6666666667 + 1.173611113

Combine like terms: -0.6666666667 + 1.173611113 = 0.5069444463
1.173611113 + -2.166666667x + x2 = 0.5069444463

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 0.5069444463

Calculate the square root of the right side: 0.712000313

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 0.712000313 and -0.712000313.

Subproblem 1
x + -1.083333334 = 0.712000313

Simplifying
x + -1.083333334 = 0.712000313

Reorder the terms:
-1.083333334 + x = 0.712000313

Solving
-1.083333334 + x = 0.712000313

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = 0.712000313 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = 0.712000313 + 1.083333334
x = 0.712000313 + 1.083333334

Combine like terms: 0.712000313 + 1.083333334 = 1.795333647
x = 1.795333647

Simplifying
x = 1.795333647

Subproblem 2
x + -1.083333334 = -0.712000313

Simplifying
x + -1.083333334 = -0.712000313

Reorder the terms:
-1.083333334 + x = -0.712000313

Solving
-1.083333334 + x = -0.712000313

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = -0.712000313 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = -0.712000313 + 1.083333334
x = -0.712000313 + 1.083333334

Combine like terms: -0.712000313 + 1.083333334 = 0.371333021
x = 0.371333021

Simplifying
x = 0.371333021

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.795333647, 0.371333021}
Solution
x = {1.795333647, 0.371333021}