15x^2+51x-9=0

Solution for 15x^2+51x-9=0 equation:

Simplifying
15x2 + 51x + -9 = 0

Reorder the terms:
-9 + 51x + 15x2 = 0

Solving
-9 + 51x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 17x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + 17x + 5x2)' equal to zero and attempt to solve:

Simplifying
-3 + 17x + 5x2 = 0

Solving
-3 + 17x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 3.4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 3.4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 3.4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 3.4x + x2 = 0 + 0.6
3.4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
3.4x + x2 = 0.6

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = 0.6 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 0.6 + 2.89

Combine like terms: 0.6 + 2.89 = 3.49
2.89 + 3.4x + x2 = 3.49

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 3.49

Calculate the square root of the right side: 1.868154169

Break this problem into two subproblems by setting 
(x + 1.7) equal to 1.868154169 and -1.868154169.

Subproblem 1
x + 1.7 = 1.868154169

Simplifying
x + 1.7 = 1.868154169

Reorder the terms:
1.7 + x = 1.868154169

Solving
1.7 + x = 1.868154169

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 1.868154169 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 1.868154169 + -1.7
x = 1.868154169 + -1.7

Combine like terms: 1.868154169 + -1.7 = 0.168154169
x = 0.168154169

Simplifying
x = 0.168154169

Subproblem 2
x + 1.7 = -1.868154169

Simplifying
x + 1.7 = -1.868154169

Reorder the terms:
1.7 + x = -1.868154169

Solving
1.7 + x = -1.868154169

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -1.868154169 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -1.868154169 + -1.7
x = -1.868154169 + -1.7

Combine like terms: -1.868154169 + -1.7 = -3.568154169
x = -3.568154169

Simplifying
x = -3.568154169

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.168154169, -3.568154169}
Solution
x = {0.168154169, -3.568154169}