12x^2-4x-30=0

Solution for 12x^2-4x-30=0 equation:

Simplifying
12x2 + -4x + -30 = 0

Reorder the terms:
-30 + -4x + 12x2 = 0

Solving
-30 + -4x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -2x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + -2x + 6x2)' equal to zero and attempt to solve:

Simplifying
-15 + -2x + 6x2 = 0

Solving
-15 + -2x + 6x2 = 0

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

Divide each side by '6'.
-2.5 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.3333333333x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.3333333333x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.3333333333x + x2 = 0 + 2.5
-0.3333333333x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.3333333333x + x2 = 2.5

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 2.5 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 2.5 + 0.02777777779

Combine like terms: 2.5 + 0.02777777779 = 2.52777777779
0.02777777779 + -0.3333333333x + x2 = 2.52777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 2.52777777779

Calculate the square root of the right side: 1.589898669

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.589898669 and -1.589898669.

Subproblem 1
x + -0.1666666667 = 1.589898669

Simplifying
x + -0.1666666667 = 1.589898669

Reorder the terms:
-0.1666666667 + x = 1.589898669

Solving
-0.1666666667 + x = 1.589898669

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 1.589898669 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 1.589898669 + 0.1666666667
x = 1.589898669 + 0.1666666667

Combine like terms: 1.589898669 + 0.1666666667 = 1.7565653357
x = 1.7565653357

Simplifying
x = 1.7565653357

Subproblem 2
x + -0.1666666667 = -1.589898669

Simplifying
x + -0.1666666667 = -1.589898669

Reorder the terms:
-0.1666666667 + x = -1.589898669

Solving
-0.1666666667 + x = -1.589898669

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -1.589898669 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -1.589898669 + 0.1666666667
x = -1.589898669 + 0.1666666667

Combine like terms: -1.589898669 + 0.1666666667 = -1.4232320023
x = -1.4232320023

Simplifying
x = -1.4232320023

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.7565653357, -1.4232320023}
Solution
x = {1.7565653357, -1.4232320023}