0=-275x^2+320x+18240

Solution for 0=-275x^2+320x+18240 equation:

Simplifying
0 = -275x2 + 320x + 18240

Reorder the terms:
0 = 18240 + 320x + -275x2

Solving
0 = 18240 + 320x + -275x2

Solving for variable 'x'.

Combine like terms: 0 + -18240 = -18240
-18240 + -320x + 275x2 = 18240 + 320x + -275x2 + -18240 + -320x + 275x2

Reorder the terms:
-18240 + -320x + 275x2 = 18240 + -18240 + 320x + -320x + -275x2 + 275x2

Combine like terms: 18240 + -18240 = 0
-18240 + -320x + 275x2 = 0 + 320x + -320x + -275x2 + 275x2
-18240 + -320x + 275x2 = 320x + -320x + -275x2 + 275x2

Combine like terms: 320x + -320x = 0
-18240 + -320x + 275x2 = 0 + -275x2 + 275x2
-18240 + -320x + 275x2 = -275x2 + 275x2

Combine like terms: -275x2 + 275x2 = 0
-18240 + -320x + 275x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3648 + -64x + 55x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3648 + -64x + 55x2)' equal to zero and attempt to solve:

Simplifying
-3648 + -64x + 55x2 = 0

Solving
-3648 + -64x + 55x2 = 0

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

Divide each side by '55'.
-66.32727273 + -1.163636364x + x2 = 0

Move the constant term to the right:

Add '66.32727273' to each side of the equation.
-66.32727273 + -1.163636364x + 66.32727273 + x2 = 0 + 66.32727273

Reorder the terms:
-66.32727273 + 66.32727273 + -1.163636364x + x2 = 0 + 66.32727273

Combine like terms: -66.32727273 + 66.32727273 = 0.00000000
0.00000000 + -1.163636364x + x2 = 0 + 66.32727273
-1.163636364x + x2 = 0 + 66.32727273

Combine like terms: 0 + 66.32727273 = 66.32727273
-1.163636364x + x2 = 66.32727273

The x term is -1.163636364x.  Take half its coefficient (-0.581818182).
Square it (0.3385123969) and add it to both sides.

Add '0.3385123969' to each side of the equation.
-1.163636364x + 0.3385123969 + x2 = 66.32727273 + 0.3385123969

Reorder the terms:
0.3385123969 + -1.163636364x + x2 = 66.32727273 + 0.3385123969

Combine like terms: 66.32727273 + 0.3385123969 = 66.6657851269
0.3385123969 + -1.163636364x + x2 = 66.6657851269

Factor a perfect square on the left side:
(x + -0.581818182)(x + -0.581818182) = 66.6657851269

Calculate the square root of the right side: 8.164911826

Break this problem into two subproblems by setting 
(x + -0.581818182) equal to 8.164911826 and -8.164911826.

Subproblem 1
x + -0.581818182 = 8.164911826

Simplifying
x + -0.581818182 = 8.164911826

Reorder the terms:
-0.581818182 + x = 8.164911826

Solving
-0.581818182 + x = 8.164911826

Solving for variable 'x'.

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

Add '0.581818182' to each side of the equation.
-0.581818182 + 0.581818182 + x = 8.164911826 + 0.581818182

Combine like terms: -0.581818182 + 0.581818182 = 0.000000000
0.000000000 + x = 8.164911826 + 0.581818182
x = 8.164911826 + 0.581818182

Combine like terms: 8.164911826 + 0.581818182 = 8.746730008
x = 8.746730008

Simplifying
x = 8.746730008

Subproblem 2
x + -0.581818182 = -8.164911826

Simplifying
x + -0.581818182 = -8.164911826

Reorder the terms:
-0.581818182 + x = -8.164911826

Solving
-0.581818182 + x = -8.164911826

Solving for variable 'x'.

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

Add '0.581818182' to each side of the equation.
-0.581818182 + 0.581818182 + x = -8.164911826 + 0.581818182

Combine like terms: -0.581818182 + 0.581818182 = 0.000000000
0.000000000 + x = -8.164911826 + 0.581818182
x = -8.164911826 + 0.581818182

Combine like terms: -8.164911826 + 0.581818182 = -7.583093644
x = -7.583093644

Simplifying
x = -7.583093644

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.746730008, -7.583093644}
Solution
x = {8.746730008, -7.583093644}