0=0.5*166.66667*x^2+60x-0.5*6*9604

Solution for 0=0.5*166.66667*x^2+60x-0.5*6*9604 equation:

Simplifying
0 = 0.5 * 166.66667x2 + 60x + -0.5 * 6 * 9604

Multiply 0.5 * 166.66667
0 = 83.333335x2 + 60x + -0.5 * 6 * 9604

Multiply -0.5 * 6
0 = 83.333335x2 + 60x + -3 * 9604

Multiply -3 * 9604
0 = 83.333335x2 + 60x + -28812

Reorder the terms:
0 = -28812 + 60x + 83.333335x2

Solving
0 = -28812 + 60x + 83.333335x2

Solving for variable 'x'.

Combine like terms: 0 + 28812 = 28812
28812 + -60x + -83.333335x2 = -28812 + 60x + 83.333335x2 + 28812 + -60x + -83.333335x2

Reorder the terms:
28812 + -60x + -83.333335x2 = -28812 + 28812 + 60x + -60x + 83.333335x2 + -83.333335x2

Combine like terms: -28812 + 28812 = 0
28812 + -60x + -83.333335x2 = 0 + 60x + -60x + 83.333335x2 + -83.333335x2
28812 + -60x + -83.333335x2 = 60x + -60x + 83.333335x2 + -83.333335x2

Combine like terms: 60x + -60x = 0
28812 + -60x + -83.333335x2 = 0 + 83.333335x2 + -83.333335x2
28812 + -60x + -83.333335x2 = 83.333335x2 + -83.333335x2

Combine like terms: 83.333335x2 + -83.333335x2 = 0.000000
28812 + -60x + -83.333335x2 = 0.000000

Begin completing the square.  Divide all terms by
-83.333335 the coefficient of the squared term: 

Divide each side by '-83.333335'.
-345.7439931 + 0.7199999856x + x2 = 0

Move the constant term to the right:

Add '345.7439931' to each side of the equation.
-345.7439931 + 0.7199999856x + 345.7439931 + x2 = 0 + 345.7439931

Reorder the terms:
-345.7439931 + 345.7439931 + 0.7199999856x + x2 = 0 + 345.7439931

Combine like terms: -345.7439931 + 345.7439931 = 0.0000000
0.0000000 + 0.7199999856x + x2 = 0 + 345.7439931
0.7199999856x + x2 = 0 + 345.7439931

Combine like terms: 0 + 345.7439931 = 345.7439931
0.7199999856x + x2 = 345.7439931

The x term is 0.7199999856x.  Take half its coefficient (0.3599999928).
Square it (0.1295999948) and add it to both sides.

Add '0.1295999948' to each side of the equation.
0.7199999856x + 0.1295999948 + x2 = 345.7439931 + 0.1295999948

Reorder the terms:
0.1295999948 + 0.7199999856x + x2 = 345.7439931 + 0.1295999948

Combine like terms: 345.7439931 + 0.1295999948 = 345.8735930948
0.1295999948 + 0.7199999856x + x2 = 345.8735930948

Factor a perfect square on the left side:
(x + 0.3599999928)(x + 0.3599999928) = 345.8735930948

Calculate the square root of the right side: 18.597677089

Break this problem into two subproblems by setting 
(x + 0.3599999928) equal to 18.597677089 and -18.597677089.

Subproblem 1
x + 0.3599999928 = 18.597677089

Simplifying
x + 0.3599999928 = 18.597677089

Reorder the terms:
0.3599999928 + x = 18.597677089

Solving
0.3599999928 + x = 18.597677089

Solving for variable 'x'.

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

Add '-0.3599999928' to each side of the equation.
0.3599999928 + -0.3599999928 + x = 18.597677089 + -0.3599999928

Combine like terms: 0.3599999928 + -0.3599999928 = 0.0000000000
0.0000000000 + x = 18.597677089 + -0.3599999928
x = 18.597677089 + -0.3599999928

Combine like terms: 18.597677089 + -0.3599999928 = 18.2376770962
x = 18.2376770962

Simplifying
x = 18.2376770962

Subproblem 2
x + 0.3599999928 = -18.597677089

Simplifying
x + 0.3599999928 = -18.597677089

Reorder the terms:
0.3599999928 + x = -18.597677089

Solving
0.3599999928 + x = -18.597677089

Solving for variable 'x'.

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

Add '-0.3599999928' to each side of the equation.
0.3599999928 + -0.3599999928 + x = -18.597677089 + -0.3599999928

Combine like terms: 0.3599999928 + -0.3599999928 = 0.0000000000
0.0000000000 + x = -18.597677089 + -0.3599999928
x = -18.597677089 + -0.3599999928

Combine like terms: -18.597677089 + -0.3599999928 = -18.9576770818
x = -18.9576770818

Simplifying
x = -18.9576770818

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.2376770962, -18.9576770818}