192x^2-160x-250=0

Solution for 192x^2-160x-250=0 equation:

Simplifying
192x2 + -160x + -250 = 0

Reorder the terms:
-250 + -160x + 192x2 = 0

Solving
-250 + -160x + 192x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + -80x + 96x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-125 + -80x + 96x2)' equal to zero and attempt to solve:

Simplifying
-125 + -80x + 96x2 = 0

Solving
-125 + -80x + 96x2 = 0

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

Divide each side by '96'.
-1.302083333 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '1.302083333' to each side of the equation.
-1.302083333 + -0.8333333333x + 1.302083333 + x2 = 0 + 1.302083333

Reorder the terms:
-1.302083333 + 1.302083333 + -0.8333333333x + x2 = 0 + 1.302083333

Combine like terms: -1.302083333 + 1.302083333 = 0.000000000
0.000000000 + -0.8333333333x + x2 = 0 + 1.302083333
-0.8333333333x + x2 = 0 + 1.302083333

Combine like terms: 0 + 1.302083333 = 1.302083333
-0.8333333333x + x2 = 1.302083333

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 1.302083333 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 1.302083333 + 0.1736111111

Combine like terms: 1.302083333 + 0.1736111111 = 1.4756944441
0.1736111111 + -0.8333333333x + x2 = 1.4756944441

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 1.4756944441

Calculate the square root of the right side: 1.214781645

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 1.214781645 and -1.214781645.

Subproblem 1
x + -0.4166666667 = 1.214781645

Simplifying
x + -0.4166666667 = 1.214781645

Reorder the terms:
-0.4166666667 + x = 1.214781645

Solving
-0.4166666667 + x = 1.214781645

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 1.214781645 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 1.214781645 + 0.4166666667
x = 1.214781645 + 0.4166666667

Combine like terms: 1.214781645 + 0.4166666667 = 1.6314483117
x = 1.6314483117

Simplifying
x = 1.6314483117

Subproblem 2
x + -0.4166666667 = -1.214781645

Simplifying
x + -0.4166666667 = -1.214781645

Reorder the terms:
-0.4166666667 + x = -1.214781645

Solving
-0.4166666667 + x = -1.214781645

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -1.214781645 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -1.214781645 + 0.4166666667
x = -1.214781645 + 0.4166666667

Combine like terms: -1.214781645 + 0.4166666667 = -0.7981149783
x = -0.7981149783

Simplifying
x = -0.7981149783

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6314483117, -0.7981149783}
Solution
x = {1.6314483117, -0.7981149783}