15x^2+7x-12=0

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Solution for 15x^2+7x-12=0 equation: 


Simplifying
15x2 + 7x + -12 = 0

Reorder the terms:
-12 + 7x + 15x2 = 0

Solving
-12 + 7x + 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 + 0.4666666667x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 0.4666666667x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 0.4666666667x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 0.4666666667x + x2 = 0 + 0.8
0.4666666667x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
0.4666666667x + x2 = 0.8

The x term is 0.4666666667x.  Take half its coefficient (0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
0.4666666667x + 0.05444444448 + x2 = 0.8 + 0.05444444448

Reorder the terms:
0.05444444448 + 0.4666666667x + x2 = 0.8 + 0.05444444448

Combine like terms: 0.8 + 0.05444444448 = 0.85444444448
0.05444444448 + 0.4666666667x + x2 = 0.85444444448

Factor a perfect square on the left side:
(x + 0.2333333334)(x + 0.2333333334) = 0.85444444448

Calculate the square root of the right side: 0.924361642

Break this problem into two subproblems by setting 
(x + 0.2333333334) equal to 0.924361642 and -0.924361642.


Subproblem 1
x + 0.2333333334 = 0.924361642

Simplifying
x + 0.2333333334 = 0.924361642

Reorder the terms:
0.2333333334 + x = 0.924361642

Solving
0.2333333334 + x = 0.924361642

Solving for variable 'x'.

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

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = 0.924361642 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = 0.924361642 + -0.2333333334
x = 0.924361642 + -0.2333333334

Combine like terms: 0.924361642 + -0.2333333334 = 0.6910283086
x = 0.6910283086

Simplifying
x = 0.6910283086


Subproblem 2
x + 0.2333333334 = -0.924361642

Simplifying
x + 0.2333333334 = -0.924361642

Reorder the terms:
0.2333333334 + x = -0.924361642

Solving
0.2333333334 + x = -0.924361642

Solving for variable 'x'.

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

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = -0.924361642 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = -0.924361642 + -0.2333333334
x = -0.924361642 + -0.2333333334

Combine like terms: -0.924361642 + -0.2333333334 = -1.1576949754
x = -1.1576949754

Simplifying
x = -1.1576949754


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6910283086, -1.1576949754}

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