3x^2-6x-124=0

Solution for 3x^2-6x-124=0 equation:

Simplifying
3x2 + -6x + -124 = 0

Reorder the terms:
-124 + -6x + 3x2 = 0

Solving
-124 + -6x + 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'.
-41.33333333 + -2x + x2 = 0

Move the constant term to the right:

Add '41.33333333' to each side of the equation.
-41.33333333 + -2x + 41.33333333 + x2 = 0 + 41.33333333

Reorder the terms:
-41.33333333 + 41.33333333 + -2x + x2 = 0 + 41.33333333

Combine like terms: -41.33333333 + 41.33333333 = 0.00000000
0.00000000 + -2x + x2 = 0 + 41.33333333
-2x + x2 = 0 + 41.33333333

Combine like terms: 0 + 41.33333333 = 41.33333333
-2x + x2 = 41.33333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 41.33333333 + 1

Reorder the terms:
1 + -2x + x2 = 41.33333333 + 1

Combine like terms: 41.33333333 + 1 = 42.33333333
1 + -2x + x2 = 42.33333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 42.33333333

Calculate the square root of the right side: 6.506407098

Break this problem into two subproblems by setting 
(x + -1) equal to 6.506407098 and -6.506407098.

Subproblem 1
x + -1 = 6.506407098

Simplifying
x + -1 = 6.506407098

Reorder the terms:
-1 + x = 6.506407098

Solving
-1 + x = 6.506407098

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6.506407098 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.506407098 + 1
x = 6.506407098 + 1

Combine like terms: 6.506407098 + 1 = 7.506407098
x = 7.506407098

Simplifying
x = 7.506407098

Subproblem 2
x + -1 = -6.506407098

Simplifying
x + -1 = -6.506407098

Reorder the terms:
-1 + x = -6.506407098

Solving
-1 + x = -6.506407098

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6.506407098 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.506407098 + 1
x = -6.506407098 + 1

Combine like terms: -6.506407098 + 1 = -5.506407098
x = -5.506407098

Simplifying
x = -5.506407098

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.506407098, -5.506407098}