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 = 0.015314892913
0.007657845304 + 0.1750182311x + x2 = 0.015314892913

Factor a perfect square on the left side:
(x + 0.08750911555)(x + 0.08750911555) = 0.015314892913

Calculate the square root of the right side: 0.123753355

Break this problem into two subproblems by setting 
(x + 0.08750911555) equal to 0.123753355 and -0.123753355.

Subproblem 1
x + 0.08750911555 = 0.123753355

Simplifying
x + 0.08750911555 = 0.123753355

Reorder the terms:
0.08750911555 + x = 0.123753355

Solving
0.08750911555 + x = 0.123753355

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 = 0.123753355 + -0.08750911555

Combine like terms: 0.08750911555 + -0.08750911555 = 0.00000000000
0.00000000000 + x = 0.123753355 + -0.08750911555
x = 0.123753355 + -0.08750911555

Combine like terms: 0.123753355 + -0.08750911555 = 0.03624423945
x = 0.03624423945

Simplifying
x = 0.03624423945

Subproblem 2
x + 0.08750911555 = -0.123753355

Simplifying
x + 0.08750911555 = -0.123753355

Reorder the terms:
0.08750911555 + x = -0.123753355

Solving
0.08750911555 + x = -0.123753355

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 = -0.123753355 + -0.08750911555

Combine like terms: 0.08750911555 + -0.08750911555 = 0.00000000000
0.00000000000 + x = -0.123753355 + -0.08750911555
x = -0.123753355 + -0.08750911555

Combine like terms: -0.123753355 + -0.08750911555 = -0.21126247055
x = -0.21126247055

Simplifying
x = -0.21126247055

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.03624423945, -0.21126247055}