0=73.5-1680x-9601(x^2)

Solution for 0=73.5-1680x-9601(x^2) equation:

Simplifying
0 = 73.5 + -1680x + -9601(x2)

Solving
0 = 73.5 + -1680x + -9601x2

Solving for variable 'x'.

Combine like terms: 0 + -73.5 = -73.5
-73.5 + 1680x + 9601x2 = 73.5 + -1680x + -9601x2 + -73.5 + 1680x + 9601x2

Reorder the terms:
-73.5 + 1680x + 9601x2 = 73.5 + -73.5 + -1680x + 1680x + -9601x2 + 9601x2

Combine like terms: 73.5 + -73.5 = 0.0
-73.5 + 1680x + 9601x2 = 0.0 + -1680x + 1680x + -9601x2 + 9601x2
-73.5 + 1680x + 9601x2 = -1680x + 1680x + -9601x2 + 9601x2

Combine like terms: -1680x + 1680x = 0
-73.5 + 1680x + 9601x2 = 0 + -9601x2 + 9601x2
-73.5 + 1680x + 9601x2 = -9601x2 + 9601x2

Combine like terms: -9601x2 + 9601x2 = 0
-73.5 + 1680x + 9601x2 = 0

Begin completing the square.  Divide all terms by
9601 the coefficient of the squared term: 

Divide each side by '9601'.
-0.007655452557 + 0.1749817727x + x2 = 0

Move the constant term to the right:

Add '0.007655452557' to each side of the equation.
-0.007655452557 + 0.1749817727x + 0.007655452557 + x2 = 0 + 0.007655452557

Reorder the terms:
-0.007655452557 + 0.007655452557 + 0.1749817727x + x2 = 0 + 0.007655452557

Combine like terms: -0.007655452557 + 0.007655452557 = 0.000000000000
0.000000000000 + 0.1749817727x + x2 = 0 + 0.007655452557
0.1749817727x + x2 = 0 + 0.007655452557

Combine like terms: 0 + 0.007655452557 = 0.007655452557
0.1749817727x + x2 = 0.007655452557

The x term is 0.1749817727x.  Take half its coefficient (0.08749088635).
Square it (0.007654655194) and add it to both sides.

Add '0.007654655194' to each side of the equation.
0.1749817727x + 0.007654655194 + x2 = 0.007655452557 + 0.007654655194

Reorder the terms:
0.007654655194 + 0.1749817727x + x2 = 0.007655452557 + 0.007654655194

Combine like terms: 0.007655452557 + 0.007654655194 = 0.015310107751
0.007654655194 + 0.1749817727x + x2 = 0.015310107751

Factor a perfect square on the left side:
(x + 0.08749088635)(x + 0.08749088635) = 0.015310107751

Calculate the square root of the right side: 0.12373402

Break this problem into two subproblems by setting 
(x + 0.08749088635) equal to 0.12373402 and -0.12373402.

Subproblem 1
x + 0.08749088635 = 0.12373402

Simplifying
x + 0.08749088635 = 0.12373402

Reorder the terms:
0.08749088635 + x = 0.12373402

Solving
0.08749088635 + x = 0.12373402

Solving for variable 'x'.

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

Add '-0.08749088635' to each side of the equation.
0.08749088635 + -0.08749088635 + x = 0.12373402 + -0.08749088635

Combine like terms: 0.08749088635 + -0.08749088635 = 0.00000000000
0.00000000000 + x = 0.12373402 + -0.08749088635
x = 0.12373402 + -0.08749088635

Combine like terms: 0.12373402 + -0.08749088635 = 0.03624313365
x = 0.03624313365

Simplifying
x = 0.03624313365

Subproblem 2
x + 0.08749088635 = -0.12373402

Simplifying
x + 0.08749088635 = -0.12373402

Reorder the terms:
0.08749088635 + x = -0.12373402

Solving
0.08749088635 + x = -0.12373402

Solving for variable 'x'.

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

Add '-0.08749088635' to each side of the equation.
0.08749088635 + -0.08749088635 + x = -0.12373402 + -0.08749088635

Combine like terms: 0.08749088635 + -0.08749088635 = 0.00000000000
0.00000000000 + x = -0.12373402 + -0.08749088635
x = -0.12373402 + -0.08749088635

Combine like terms: -0.12373402 + -0.08749088635 = -0.21122490635
x = -0.21122490635

Simplifying
x = -0.21122490635

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.03624313365, -0.21122490635}