15x^2+12x-8=0

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Solution for 15x^2+12x-8=0 equation: 


Simplifying
15x2 + 12x + -8 = 0

Reorder the terms:
-8 + 12x + 15x2 = 0

Solving
-8 + 12x + 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'.
-0.5333333333 + 0.8x + x2 = 0

Move the constant term to the right:

Add '0.5333333333' to each side of the equation.
-0.5333333333 + 0.8x + 0.5333333333 + x2 = 0 + 0.5333333333

Reorder the terms:
-0.5333333333 + 0.5333333333 + 0.8x + x2 = 0 + 0.5333333333

Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000
0.0000000000 + 0.8x + x2 = 0 + 0.5333333333
0.8x + x2 = 0 + 0.5333333333

Combine like terms: 0 + 0.5333333333 = 0.5333333333
0.8x + x2 = 0.5333333333

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.5333333333 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.5333333333 + 0.16

Combine like terms: 0.5333333333 + 0.16 = 0.6933333333
0.16 + 0.8x + x2 = 0.6933333333

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.6933333333

Calculate the square root of the right side: 0.8326664

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.8326664 and -0.8326664.


Subproblem 1
x + 0.4 = 0.8326664

Simplifying
x + 0.4 = 0.8326664

Reorder the terms:
0.4 + x = 0.8326664

Solving
0.4 + x = 0.8326664

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 0.8326664 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.8326664 + -0.4
x = 0.8326664 + -0.4

Combine like terms: 0.8326664 + -0.4 = 0.4326664
x = 0.4326664

Simplifying
x = 0.4326664


Subproblem 2
x + 0.4 = -0.8326664

Simplifying
x + 0.4 = -0.8326664

Reorder the terms:
0.4 + x = -0.8326664

Solving
0.4 + x = -0.8326664

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -0.8326664 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.8326664 + -0.4
x = -0.8326664 + -0.4

Combine like terms: -0.8326664 + -0.4 = -1.2326664
x = -1.2326664

Simplifying
x = -1.2326664


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4326664, -1.2326664}

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