6x^2-10x-104=0

Solution for 6x^2-10x-104=0 equation:

Simplifying
6x2 + -10x + -104 = 0

Reorder the terms:
-104 + -10x + 6x2 = 0

Solving
-104 + -10x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-52 + -5x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-52 + -5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-52 + -5x + 3x2 = 0

Solving
-52 + -5x + 3x2 = 0

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

Divide each side by '3'.
-17.33333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '17.33333333' to each side of the equation.
-17.33333333 + -1.666666667x + 17.33333333 + x2 = 0 + 17.33333333

Reorder the terms:
-17.33333333 + 17.33333333 + -1.666666667x + x2 = 0 + 17.33333333

Combine like terms: -17.33333333 + 17.33333333 = 0.00000000
0.00000000 + -1.666666667x + x2 = 0 + 17.33333333
-1.666666667x + x2 = 0 + 17.33333333

Combine like terms: 0 + 17.33333333 = 17.33333333
-1.666666667x + x2 = 17.33333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 17.33333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 17.33333333 + 0.6944444447

Combine like terms: 17.33333333 + 0.6944444447 = 18.0277777747
0.6944444447 + -1.666666667x + x2 = 18.0277777747

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 18.0277777747

Calculate the square root of the right side: 4.245913067

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 4.245913067 and -4.245913067.

Subproblem 1
x + -0.8333333335 = 4.245913067

Simplifying
x + -0.8333333335 = 4.245913067

Reorder the terms:
-0.8333333335 + x = 4.245913067

Solving
-0.8333333335 + x = 4.245913067

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 4.245913067 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 4.245913067 + 0.8333333335
x = 4.245913067 + 0.8333333335

Combine like terms: 4.245913067 + 0.8333333335 = 5.0792464005
x = 5.0792464005

Simplifying
x = 5.0792464005

Subproblem 2
x + -0.8333333335 = -4.245913067

Simplifying
x + -0.8333333335 = -4.245913067

Reorder the terms:
-0.8333333335 + x = -4.245913067

Solving
-0.8333333335 + x = -4.245913067

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -4.245913067 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -4.245913067 + 0.8333333335
x = -4.245913067 + 0.8333333335

Combine like terms: -4.245913067 + 0.8333333335 = -3.4125797335
x = -3.4125797335

Simplifying
x = -3.4125797335

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.0792464005, -3.4125797335}
Solution
x = {5.0792464005, -3.4125797335}