15x^2+20x-12=0

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Solution for 15x^2+20x-12=0 equation: 


Simplifying
15x2 + 20x + -12 = 0

Reorder the terms:
-12 + 20x + 15x2 = 0

Solving
-12 + 20x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.8 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 1.333333333x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 1.333333333x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 1.333333333x + x2 = 0 + 0.8
1.333333333x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
1.333333333x + x2 = 0.8

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 0.8 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 0.8 + 0.4444444442

Combine like terms: 0.8 + 0.4444444442 = 1.2444444442
0.4444444442 + 1.333333333x + x2 = 1.2444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 1.2444444442

Calculate the square root of the right side: 1.115546702

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.115546702 and -1.115546702.


Subproblem 1
x + 0.6666666665 = 1.115546702

Simplifying
x + 0.6666666665 = 1.115546702

Reorder the terms:
0.6666666665 + x = 1.115546702

Solving
0.6666666665 + x = 1.115546702

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 1.115546702 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.115546702 + -0.6666666665
x = 1.115546702 + -0.6666666665

Combine like terms: 1.115546702 + -0.6666666665 = 0.4488800355
x = 0.4488800355

Simplifying
x = 0.4488800355


Subproblem 2
x + 0.6666666665 = -1.115546702

Simplifying
x + 0.6666666665 = -1.115546702

Reorder the terms:
0.6666666665 + x = -1.115546702

Solving
0.6666666665 + x = -1.115546702

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -1.115546702 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.115546702 + -0.6666666665
x = -1.115546702 + -0.6666666665

Combine like terms: -1.115546702 + -0.6666666665 = -1.7822133685
x = -1.7822133685

Simplifying
x = -1.7822133685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4488800355, -1.7822133685}

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