15x^2+10x-9=0

Solution for 15x^2+10x-9=0 equation:

Simplifying
15x2 + 10x + -9 = 0

Reorder the terms:
-9 + 10x + 15x2 = 0

Solving
-9 + 10x + 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'.
-0.6 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.6666666667x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.6666666667x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.6666666667x + x2 = 0 + 0.6
0.6666666667x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.6666666667x + x2 = 0.6

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.6 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.6 + 0.1111111112

Combine like terms: 0.6 + 0.1111111112 = 0.7111111112
0.1111111112 + 0.6666666667x + x2 = 0.7111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.7111111112

Calculate the square root of the right side: 0.843274043

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.843274043 and -0.843274043.

Subproblem 1
x + 0.3333333334 = 0.843274043

Simplifying
x + 0.3333333334 = 0.843274043

Reorder the terms:
0.3333333334 + x = 0.843274043

Solving
0.3333333334 + x = 0.843274043

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.843274043 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.843274043 + -0.3333333334
x = 0.843274043 + -0.3333333334

Combine like terms: 0.843274043 + -0.3333333334 = 0.5099407096
x = 0.5099407096

Simplifying
x = 0.5099407096

Subproblem 2
x + 0.3333333334 = -0.843274043

Simplifying
x + 0.3333333334 = -0.843274043

Reorder the terms:
0.3333333334 + x = -0.843274043

Solving
0.3333333334 + x = -0.843274043

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.843274043 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.843274043 + -0.3333333334
x = -0.843274043 + -0.3333333334

Combine like terms: -0.843274043 + -0.3333333334 = -1.1766073764
x = -1.1766073764

Simplifying
x = -1.1766073764

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5099407096, -1.1766073764}