3x^2-12x-8=0

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Solution for 3x^2-12x-8=0 equation: 


Simplifying
3x2 + -12x + -8 = 0

Reorder the terms:
-8 + -12x + 3x2 = 0

Solving
-8 + -12x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -4x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -4x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + 2.666666667
-4x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-4x + x2 = 2.666666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2.666666667 + 4

Reorder the terms:
4 + -4x + x2 = 2.666666667 + 4

Combine like terms: 2.666666667 + 4 = 6.666666667
4 + -4x + x2 = 6.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6.666666667

Calculate the square root of the right side: 2.581988898

Break this problem into two subproblems by setting 
(x + -2) equal to 2.581988898 and -2.581988898.


Subproblem 1
x + -2 = 2.581988898

Simplifying
x + -2 = 2.581988898

Reorder the terms:
-2 + x = 2.581988898

Solving
-2 + x = 2.581988898

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.581988898 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.581988898 + 2
x = 2.581988898 + 2

Combine like terms: 2.581988898 + 2 = 4.581988898
x = 4.581988898

Simplifying
x = 4.581988898


Subproblem 2
x + -2 = -2.581988898

Simplifying
x + -2 = -2.581988898

Reorder the terms:
-2 + x = -2.581988898

Solving
-2 + x = -2.581988898

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.581988898 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.581988898 + 2
x = -2.581988898 + 2

Combine like terms: -2.581988898 + 2 = -0.581988898
x = -0.581988898

Simplifying
x = -0.581988898


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.581988898, -0.581988898}

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