2x^2-48x-240=0

Solution for 2x^2-48x-240=0 equation:

Simplifying
2x2 + -48x + -240 = 0

Reorder the terms:
-240 + -48x + 2x2 = 0

Solving
-240 + -48x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + -24x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-120 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + -24x + x2 = 0

Solving
-120 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -24x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -24x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -24x + x2 = 0 + 120
-24x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-24x + x2 = 120

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = 120 + 144

Reorder the terms:
144 + -24x + x2 = 120 + 144

Combine like terms: 120 + 144 = 264
144 + -24x + x2 = 264

Factor a perfect square on the left side:
(x + -12)(x + -12) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(x + -12) equal to 16.248076809 and -16.248076809.

Subproblem 1
x + -12 = 16.248076809

Simplifying
x + -12 = 16.248076809

Reorder the terms:
-12 + x = 16.248076809

Solving
-12 + x = 16.248076809

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 16.248076809 + 12

Combine like terms: -12 + 12 = 0
0 + x = 16.248076809 + 12
x = 16.248076809 + 12

Combine like terms: 16.248076809 + 12 = 28.248076809
x = 28.248076809

Simplifying
x = 28.248076809

Subproblem 2
x + -12 = -16.248076809

Simplifying
x + -12 = -16.248076809

Reorder the terms:
-12 + x = -16.248076809

Solving
-12 + x = -16.248076809

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -16.248076809 + 12

Combine like terms: -12 + 12 = 0
0 + x = -16.248076809 + 12
x = -16.248076809 + 12

Combine like terms: -16.248076809 + 12 = -4.248076809
x = -4.248076809

Simplifying
x = -4.248076809

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.248076809, -4.248076809}
Solution
x = {28.248076809, -4.248076809}