15000=-88x^2+17108x-813360

Solution for 15000=-88x^2+17108x-813360 equation:

Simplifying
15000 = -88x2 + 17108x + -813360

Reorder the terms:
15000 = -813360 + 17108x + -88x2

Solving
15000 = -813360 + 17108x + -88x2

Solving for variable 'x'.

Combine like terms: 15000 + 813360 = 828360
828360 + -17108x + 88x2 = -813360 + 17108x + -88x2 + 813360 + -17108x + 88x2

Reorder the terms:
828360 + -17108x + 88x2 = -813360 + 813360 + 17108x + -17108x + -88x2 + 88x2

Combine like terms: -813360 + 813360 = 0
828360 + -17108x + 88x2 = 0 + 17108x + -17108x + -88x2 + 88x2
828360 + -17108x + 88x2 = 17108x + -17108x + -88x2 + 88x2

Combine like terms: 17108x + -17108x = 0
828360 + -17108x + 88x2 = 0 + -88x2 + 88x2
828360 + -17108x + 88x2 = -88x2 + 88x2

Combine like terms: -88x2 + 88x2 = 0
828360 + -17108x + 88x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(207090 + -4277x + 22x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(207090 + -4277x + 22x2)' equal to zero and attempt to solve:

Simplifying
207090 + -4277x + 22x2 = 0

Solving
207090 + -4277x + 22x2 = 0

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

Divide each side by '22'.
9413.181818 + -194.4090909x + x2 = 0

Move the constant term to the right:

Add '-9413.181818' to each side of the equation.
9413.181818 + -194.4090909x + -9413.181818 + x2 = 0 + -9413.181818

Reorder the terms:
9413.181818 + -9413.181818 + -194.4090909x + x2 = 0 + -9413.181818

Combine like terms: 9413.181818 + -9413.181818 = 0.000000
0.000000 + -194.4090909x + x2 = 0 + -9413.181818
-194.4090909x + x2 = 0 + -9413.181818

Combine like terms: 0 + -9413.181818 = -9413.181818
-194.4090909x + x2 = -9413.181818

The x term is -194.4090909x.  Take half its coefficient (-97.20454545).
Square it (9448.723656) and add it to both sides.

Add '9448.723656' to each side of the equation.
-194.4090909x + 9448.723656 + x2 = -9413.181818 + 9448.723656

Reorder the terms:
9448.723656 + -194.4090909x + x2 = -9413.181818 + 9448.723656

Combine like terms: -9413.181818 + 9448.723656 = 35.541838
9448.723656 + -194.4090909x + x2 = 35.541838

Factor a perfect square on the left side:
(x + -97.20454545)(x + -97.20454545) = 35.541838

Calculate the square root of the right side: 5.961697577

Break this problem into two subproblems by setting 
(x + -97.20454545) equal to 5.961697577 and -5.961697577.

Subproblem 1
x + -97.20454545 = 5.961697577

Simplifying
x + -97.20454545 = 5.961697577

Reorder the terms:
-97.20454545 + x = 5.961697577

Solving
-97.20454545 + x = 5.961697577

Solving for variable 'x'.

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

Add '97.20454545' to each side of the equation.
-97.20454545 + 97.20454545 + x = 5.961697577 + 97.20454545

Combine like terms: -97.20454545 + 97.20454545 = 0.00000000
0.00000000 + x = 5.961697577 + 97.20454545
x = 5.961697577 + 97.20454545

Combine like terms: 5.961697577 + 97.20454545 = 103.166243027
x = 103.166243027

Simplifying
x = 103.166243027

Subproblem 2
x + -97.20454545 = -5.961697577

Simplifying
x + -97.20454545 = -5.961697577

Reorder the terms:
-97.20454545 + x = -5.961697577

Solving
-97.20454545 + x = -5.961697577

Solving for variable 'x'.

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

Add '97.20454545' to each side of the equation.
-97.20454545 + 97.20454545 + x = -5.961697577 + 97.20454545

Combine like terms: -97.20454545 + 97.20454545 = 0.00000000
0.00000000 + x = -5.961697577 + 97.20454545
x = -5.961697577 + 97.20454545

Combine like terms: -5.961697577 + 97.20454545 = 91.242847873
x = 91.242847873

Simplifying
x = 91.242847873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {103.166243027, 91.242847873}
Solution
x = {103.166243027, 91.242847873}