3x^2+20x-12=0

Solution for 3x^2+20x-12=0 equation:

Simplifying
3x2 + 20x + -12 = 0

Reorder the terms:
-12 + 20x + 3x2 = 0

Solving
-12 + 20x + 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'.
-4 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6.666666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 6.666666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6.666666667x + x2 = 0 + 4
6.666666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
6.666666667x + x2 = 4

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 4 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 4 + 11.11111112

Combine like terms: 4 + 11.11111112 = 15.11111112
11.11111112 + 6.666666667x + x2 = 15.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 15.11111112

Calculate the square root of the right side: 3.887301264

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 3.887301264 and -3.887301264.

Subproblem 1
x + 3.333333334 = 3.887301264

Simplifying
x + 3.333333334 = 3.887301264

Reorder the terms:
3.333333334 + x = 3.887301264

Solving
3.333333334 + x = 3.887301264

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 3.887301264 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 3.887301264 + -3.333333334
x = 3.887301264 + -3.333333334

Combine like terms: 3.887301264 + -3.333333334 = 0.55396793
x = 0.55396793

Simplifying
x = 0.55396793

Subproblem 2
x + 3.333333334 = -3.887301264

Simplifying
x + 3.333333334 = -3.887301264

Reorder the terms:
3.333333334 + x = -3.887301264

Solving
3.333333334 + x = -3.887301264

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -3.887301264 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -3.887301264 + -3.333333334
x = -3.887301264 + -3.333333334

Combine like terms: -3.887301264 + -3.333333334 = -7.220634598
x = -7.220634598

Simplifying
x = -7.220634598

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.55396793, -7.220634598}