50x^2-200x-60=0

Solution for 50x^2-200x-60=0 equation:

Simplifying
50x2 + -200x + -60 = 0

Reorder the terms:
-60 + -200x + 50x2 = 0

Solving
-60 + -200x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-6 + -20x + 5x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-6 + -20x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + -20x + 5x2 = 0

Solving
-6 + -20x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + -4x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -4x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -4x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -4x + x2 = 0 + 1.2
-4x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-4x + x2 = 1.2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.2 + 4

Reorder the terms:
4 + -4x + x2 = 1.2 + 4

Combine like terms: 1.2 + 4 = 5.2
4 + -4x + x2 = 5.2

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.2

Calculate the square root of the right side: 2.28035085

Break this problem into two subproblems by setting 
(x + -2) equal to 2.28035085 and -2.28035085.

Subproblem 1
x + -2 = 2.28035085

Simplifying
x + -2 = 2.28035085

Reorder the terms:
-2 + x = 2.28035085

Solving
-2 + x = 2.28035085

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.28035085 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.28035085 + 2
x = 2.28035085 + 2

Combine like terms: 2.28035085 + 2 = 4.28035085
x = 4.28035085

Simplifying
x = 4.28035085

Subproblem 2
x + -2 = -2.28035085

Simplifying
x + -2 = -2.28035085

Reorder the terms:
-2 + x = -2.28035085

Solving
-2 + x = -2.28035085

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.28035085 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.28035085 + 2
x = -2.28035085 + 2

Combine like terms: -2.28035085 + 2 = -0.28035085
x = -0.28035085

Simplifying
x = -0.28035085

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.28035085, -0.28035085}
Solution
x = {4.28035085, -0.28035085}