6x^2-8x-104=0

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Solution for 6x^2-8x-104=0 equation: 


Simplifying
6x2 + -8x + -104 = 0

Reorder the terms:
-104 + -8x + 6x2 = 0

Solving
-104 + -8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-52 + -4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-52 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-52 + -4x + 3x2 = 0

Solving
-52 + -4x + 3x2 = 0

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

Divide each side by '3'.
-17.33333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '17.33333333' to each side of the equation.
-17.33333333 + -1.333333333x + 17.33333333 + x2 = 0 + 17.33333333

Reorder the terms:
-17.33333333 + 17.33333333 + -1.333333333x + x2 = 0 + 17.33333333

Combine like terms: -17.33333333 + 17.33333333 = 0.00000000
0.00000000 + -1.333333333x + x2 = 0 + 17.33333333
-1.333333333x + x2 = 0 + 17.33333333

Combine like terms: 0 + 17.33333333 = 17.33333333
-1.333333333x + x2 = 17.33333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 17.33333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 17.33333333 + 0.4444444442

Combine like terms: 17.33333333 + 0.4444444442 = 17.7777777742
0.4444444442 + -1.333333333x + x2 = 17.7777777742

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 17.7777777742

Calculate the square root of the right side: 4.216370213

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 4.216370213 and -4.216370213.


Subproblem 1
x + -0.6666666665 = 4.216370213

Simplifying
x + -0.6666666665 = 4.216370213

Reorder the terms:
-0.6666666665 + x = 4.216370213

Solving
-0.6666666665 + x = 4.216370213

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 4.216370213 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 4.216370213 + 0.6666666665
x = 4.216370213 + 0.6666666665

Combine like terms: 4.216370213 + 0.6666666665 = 4.8830368795
x = 4.8830368795

Simplifying
x = 4.8830368795


Subproblem 2
x + -0.6666666665 = -4.216370213

Simplifying
x + -0.6666666665 = -4.216370213

Reorder the terms:
-0.6666666665 + x = -4.216370213

Solving
-0.6666666665 + x = -4.216370213

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -4.216370213 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -4.216370213 + 0.6666666665
x = -4.216370213 + 0.6666666665

Combine like terms: -4.216370213 + 0.6666666665 = -3.5497035465
x = -3.5497035465

Simplifying
x = -3.5497035465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.8830368795, -3.5497035465}
Solution
x = {4.8830368795, -3.5497035465}

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