50x-120x(92-x)=8340

Solution for 50x-120x(92-x)=8340 equation:

Simplifying
50x + -120x(92 + -1x) = 8340
50x + (92 * -120x + -1x * -120x) = 8340
50x + (-11040x + 120x2) = 8340

Combine like terms: 50x + -11040x = -10990x
-10990x + 120x2 = 8340

Solving
-10990x + 120x2 = 8340

Solving for variable 'x'.

Reorder the terms:
-8340 + -10990x + 120x2 = 8340 + -8340

Combine like terms: 8340 + -8340 = 0
-8340 + -10990x + 120x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-834 + -1099x + 12x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-834 + -1099x + 12x2)' equal to zero and attempt to solve:

Simplifying
-834 + -1099x + 12x2 = 0

Solving
-834 + -1099x + 12x2 = 0

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

Divide each side by '12'.
-69.5 + -91.58333333x + x2 = 0

Move the constant term to the right:

Add '69.5' to each side of the equation.
-69.5 + -91.58333333x + 69.5 + x2 = 0 + 69.5

Reorder the terms:
-69.5 + 69.5 + -91.58333333x + x2 = 0 + 69.5

Combine like terms: -69.5 + 69.5 = 0.0
0.0 + -91.58333333x + x2 = 0 + 69.5
-91.58333333x + x2 = 0 + 69.5

Combine like terms: 0 + 69.5 = 69.5
-91.58333333x + x2 = 69.5

The x term is -91.58333333x.  Take half its coefficient (-45.79166667).
Square it (2096.876736) and add it to both sides.

Add '2096.876736' to each side of the equation.
-91.58333333x + 2096.876736 + x2 = 69.5 + 2096.876736

Reorder the terms:
2096.876736 + -91.58333333x + x2 = 69.5 + 2096.876736

Combine like terms: 69.5 + 2096.876736 = 2166.376736
2096.876736 + -91.58333333x + x2 = 2166.376736

Factor a perfect square on the left side:
(x + -45.79166667)(x + -45.79166667) = 2166.376736

Calculate the square root of the right side: 46.544352353

Break this problem into two subproblems by setting 
(x + -45.79166667) equal to 46.544352353 and -46.544352353.

Subproblem 1
x + -45.79166667 = 46.544352353

Simplifying
x + -45.79166667 = 46.544352353

Reorder the terms:
-45.79166667 + x = 46.544352353

Solving
-45.79166667 + x = 46.544352353

Solving for variable 'x'.

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

Add '45.79166667' to each side of the equation.
-45.79166667 + 45.79166667 + x = 46.544352353 + 45.79166667

Combine like terms: -45.79166667 + 45.79166667 = 0.00000000
0.00000000 + x = 46.544352353 + 45.79166667
x = 46.544352353 + 45.79166667

Combine like terms: 46.544352353 + 45.79166667 = 92.336019023
x = 92.336019023

Simplifying
x = 92.336019023

Subproblem 2
x + -45.79166667 = -46.544352353

Simplifying
x + -45.79166667 = -46.544352353

Reorder the terms:
-45.79166667 + x = -46.544352353

Solving
-45.79166667 + x = -46.544352353

Solving for variable 'x'.

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

Add '45.79166667' to each side of the equation.
-45.79166667 + 45.79166667 + x = -46.544352353 + 45.79166667

Combine like terms: -45.79166667 + 45.79166667 = 0.00000000
0.00000000 + x = -46.544352353 + 45.79166667
x = -46.544352353 + 45.79166667

Combine like terms: -46.544352353 + 45.79166667 = -0.752685683
x = -0.752685683

Simplifying
x = -0.752685683

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {92.336019023, -0.752685683}
Solution
x = {92.336019023, -0.752685683}