15x^2+51x-18=0

Solution for 15x^2+51x-18=0 equation:

Simplifying
15x2 + 51x + -18 = 0

Reorder the terms:
-18 + 51x + 15x2 = 0

Solving
-18 + 51x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 17x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 17x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + 17x + 5x2 = 0

Solving
-6 + 17x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + 3.4x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 3.4x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 3.4x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 3.4x + x2 = 0 + 1.2
3.4x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
3.4x + x2 = 1.2

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 = 1.2 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 1.2 + 2.89

Combine like terms: 1.2 + 2.89 = 4.09
2.89 + 3.4x + x2 = 4.09

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 4.09

Calculate the square root of the right side: 2.022374842

Break this problem into two subproblems by setting 
(x + 1.7) equal to 2.022374842 and -2.022374842.

Subproblem 1
x + 1.7 = 2.022374842

Simplifying
x + 1.7 = 2.022374842

Reorder the terms:
1.7 + x = 2.022374842

Solving
1.7 + x = 2.022374842

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 = 2.022374842 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 2.022374842 + -1.7
x = 2.022374842 + -1.7

Combine like terms: 2.022374842 + -1.7 = 0.322374842
x = 0.322374842

Simplifying
x = 0.322374842

Subproblem 2
x + 1.7 = -2.022374842

Simplifying
x + 1.7 = -2.022374842

Reorder the terms:
1.7 + x = -2.022374842

Solving
1.7 + x = -2.022374842

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 = -2.022374842 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -2.022374842 + -1.7
x = -2.022374842 + -1.7

Combine like terms: -2.022374842 + -1.7 = -3.722374842
x = -3.722374842

Simplifying
x = -3.722374842

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.322374842, -3.722374842}
Solution
x = {0.322374842, -3.722374842}