15x^2+9x-1=0

Solution for 15x^2+9x-1=0 equation:

Simplifying
15x2 + 9x + -1 = 0

Reorder the terms:
-1 + 9x + 15x2 = 0

Solving
-1 + 9x + 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'.
-0.06666666667 + 0.6x + x2 = 0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + 0.6x + 0.06666666667 + x2 = 0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + 0.6x + x2 = 0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + 0.6x + x2 = 0 + 0.06666666667
0.6x + x2 = 0 + 0.06666666667

Combine like terms: 0 + 0.06666666667 = 0.06666666667
0.6x + x2 = 0.06666666667

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.06666666667 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.06666666667 + 0.09

Combine like terms: 0.06666666667 + 0.09 = 0.15666666667
0.09 + 0.6x + x2 = 0.15666666667

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.15666666667

Calculate the square root of the right side: 0.395811403

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.395811403 and -0.395811403.

Subproblem 1
x + 0.3 = 0.395811403

Simplifying
x + 0.3 = 0.395811403

Reorder the terms:
0.3 + x = 0.395811403

Solving
0.3 + x = 0.395811403

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 0.395811403 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.395811403 + -0.3
x = 0.395811403 + -0.3

Combine like terms: 0.395811403 + -0.3 = 0.095811403
x = 0.095811403

Simplifying
x = 0.095811403

Subproblem 2
x + 0.3 = -0.395811403

Simplifying
x + 0.3 = -0.395811403

Reorder the terms:
0.3 + x = -0.395811403

Solving
0.3 + x = -0.395811403

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -0.395811403 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.395811403 + -0.3
x = -0.395811403 + -0.3

Combine like terms: -0.395811403 + -0.3 = -0.695811403
x = -0.695811403

Simplifying
x = -0.695811403

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.095811403, -0.695811403}