0=73.5-1680x+9599(x^2)

Solution for 0=73.5-1680x+9599(x^2) equation:

Simplifying
0 = 73.5 + -1680x + 9599(x2)

Solving
0 = 73.5 + -1680x + 9599x2

Solving for variable 'x'.

Combine like terms: 0 + -73.5 = -73.5
-73.5 + 1680x + -9599x2 = 73.5 + -1680x + 9599x2 + -73.5 + 1680x + -9599x2

Reorder the terms:
-73.5 + 1680x + -9599x2 = 73.5 + -73.5 + -1680x + 1680x + 9599x2 + -9599x2

Combine like terms: 73.5 + -73.5 = 0.0
-73.5 + 1680x + -9599x2 = 0.0 + -1680x + 1680x + 9599x2 + -9599x2
-73.5 + 1680x + -9599x2 = -1680x + 1680x + 9599x2 + -9599x2

Combine like terms: -1680x + 1680x = 0
-73.5 + 1680x + -9599x2 = 0 + 9599x2 + -9599x2
-73.5 + 1680x + -9599x2 = 9599x2 + -9599x2

Combine like terms: 9599x2 + -9599x2 = 0
-73.5 + 1680x + -9599x2 = 0

Begin completing the square.  Divide all terms by
-9599 the coefficient of the squared term: 

Divide each side by '-9599'.
0.007657047609 + -0.1750182311x + x2 = 0

Move the constant term to the right:

Add '-0.007657047609' to each side of the equation.
0.007657047609 + -0.1750182311x + -0.007657047609 + x2 = 0 + -0.007657047609

Reorder the terms:
0.007657047609 + -0.007657047609 + -0.1750182311x + x2 = 0 + -0.007657047609

Combine like terms: 0.007657047609 + -0.007657047609 = 0.000000000000
0.000000000000 + -0.1750182311x + x2 = 0 + -0.007657047609
-0.1750182311x + x2 = 0 + -0.007657047609

Combine like terms: 0 + -0.007657047609 = -0.007657047609
-0.1750182311x + x2 = -0.007657047609

The x term is -0.1750182311x.  Take half its coefficient (-0.08750911555).
Square it (0.007657845304) and add it to both sides.

Add '0.007657845304' to each side of the equation.
-0.1750182311x + 0.007657845304 + x2 = -0.007657047609 + 0.007657845304

Reorder the terms:
0.007657845304 + -0.1750182311x + x2 = -0.007657047609 + 0.007657845304

Combine like terms: -0.007657047609 + 0.007657845304 = 0.000000797695
0.007657845304 + -0.1750182311x + x2 = 0.000000797695

Factor a perfect square on the left side:
(x + -0.08750911555)(x + -0.08750911555) = 0.000000797695

Calculate the square root of the right side: 0.000893138

Break this problem into two subproblems by setting 
(x + -0.08750911555) equal to 0.000893138 and -0.000893138.

Subproblem 1
x + -0.08750911555 = 0.000893138

Simplifying
x + -0.08750911555 = 0.000893138

Reorder the terms:
-0.08750911555 + x = 0.000893138

Solving
-0.08750911555 + x = 0.000893138

Solving for variable 'x'.

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

Add '0.08750911555' to each side of the equation.
-0.08750911555 + 0.08750911555 + x = 0.000893138 + 0.08750911555

Combine like terms: -0.08750911555 + 0.08750911555 = 0.00000000000
0.00000000000 + x = 0.000893138 + 0.08750911555
x = 0.000893138 + 0.08750911555

Combine like terms: 0.000893138 + 0.08750911555 = 0.08840225355
x = 0.08840225355

Simplifying
x = 0.08840225355

Subproblem 2
x + -0.08750911555 = -0.000893138

Simplifying
x + -0.08750911555 = -0.000893138

Reorder the terms:
-0.08750911555 + x = -0.000893138

Solving
-0.08750911555 + x = -0.000893138

Solving for variable 'x'.

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

Add '0.08750911555' to each side of the equation.
-0.08750911555 + 0.08750911555 + x = -0.000893138 + 0.08750911555

Combine like terms: -0.08750911555 + 0.08750911555 = 0.00000000000
0.00000000000 + x = -0.000893138 + 0.08750911555
x = -0.000893138 + 0.08750911555

Combine like terms: -0.000893138 + 0.08750911555 = 0.08661597755
x = 0.08661597755

Simplifying
x = 0.08661597755

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.08840225355, 0.08661597755}