0=3x^2+8x-12

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

Simplifying
0 = 3x2 + 8x + -12

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

Solving
0 = -12 + 8x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + -8x + -3x2 = -12 + 8x + 3x2 + 12 + -8x + -3x2

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

Combine like terms: -12 + 12 = 0
12 + -8x + -3x2 = 0 + 8x + -8x + 3x2 + -3x2
12 + -8x + -3x2 = 8x + -8x + 3x2 + -3x2

Combine like terms: 8x + -8x = 0
12 + -8x + -3x2 = 0 + 3x2 + -3x2
12 + -8x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + -8x + -3x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 4 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 4 + 1.777777780

Combine like terms: 4 + 1.777777780 = 5.77777778
1.777777780 + 2.666666667x + x2 = 5.77777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 5.77777778

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 2.403700851 and -2.403700851.

Subproblem 1
x + 1.333333334 = 2.403700851

Simplifying
x + 1.333333334 = 2.403700851

Reorder the terms:
1.333333334 + x = 2.403700851

Solving
1.333333334 + x = 2.403700851

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 2.403700851 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 2.403700851 + -1.333333334
x = 2.403700851 + -1.333333334

Combine like terms: 2.403700851 + -1.333333334 = 1.070367517
x = 1.070367517

Simplifying
x = 1.070367517

Subproblem 2
x + 1.333333334 = -2.403700851

Simplifying
x + 1.333333334 = -2.403700851

Reorder the terms:
1.333333334 + x = -2.403700851

Solving
1.333333334 + x = -2.403700851

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -2.403700851 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -2.403700851 + -1.333333334
x = -2.403700851 + -1.333333334

Combine like terms: -2.403700851 + -1.333333334 = -3.737034185
x = -3.737034185

Simplifying
x = -3.737034185

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.070367517, -3.737034185}