15x^2-90x-1800=0

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Solution for 15x^2-90x-1800=0 equation: 


Simplifying
15x2 + -90x + -1800 = 0

Reorder the terms:
-1800 + -90x + 15x2 = 0

Solving
-1800 + -90x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-120 + -6x + x2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-120 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + -6x + x2 = 0

Solving
-120 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -6x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -6x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -6x + x2 = 0 + 120
-6x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-6x + x2 = 120

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 120 + 9

Reorder the terms:
9 + -6x + x2 = 120 + 9

Combine like terms: 120 + 9 = 129
9 + -6x + x2 = 129

Factor a perfect square on the left side:
(x + -3)(x + -3) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(x + -3) equal to 11.357816692 and -11.357816692.


Subproblem 1
x + -3 = 11.357816692

Simplifying
x + -3 = 11.357816692

Reorder the terms:
-3 + x = 11.357816692

Solving
-3 + x = 11.357816692

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 11.357816692 + 3

Combine like terms: -3 + 3 = 0
0 + x = 11.357816692 + 3
x = 11.357816692 + 3

Combine like terms: 11.357816692 + 3 = 14.357816692
x = 14.357816692

Simplifying
x = 14.357816692


Subproblem 2
x + -3 = -11.357816692

Simplifying
x + -3 = -11.357816692

Reorder the terms:
-3 + x = -11.357816692

Solving
-3 + x = -11.357816692

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -11.357816692 + 3

Combine like terms: -3 + 3 = 0
0 + x = -11.357816692 + 3
x = -11.357816692 + 3

Combine like terms: -11.357816692 + 3 = -8.357816692
x = -8.357816692

Simplifying
x = -8.357816692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.357816692, -8.357816692}
Solution
x = {14.357816692, -8.357816692}

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