20x^2+112x-24=0

Solution for 20x^2+112x-24=0 equation:

Simplifying
20x2 + 112x + -24 = 0

Reorder the terms:
-24 + 112x + 20x2 = 0

Solving
-24 + 112x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 28x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + 28x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + 28x + 5x2 = 0

Solving
-6 + 28x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + 5.6x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 5.6x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 5.6x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 5.6x + x2 = 0 + 1.2
5.6x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
5.6x + x2 = 1.2

The x term is 5.6x.  Take half its coefficient (2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
5.6x + 7.84 + x2 = 1.2 + 7.84

Reorder the terms:
7.84 + 5.6x + x2 = 1.2 + 7.84

Combine like terms: 1.2 + 7.84 = 9.04
7.84 + 5.6x + x2 = 9.04

Factor a perfect square on the left side:
(x + 2.8)(x + 2.8) = 9.04

Calculate the square root of the right side: 3.006659276

Break this problem into two subproblems by setting 
(x + 2.8) equal to 3.006659276 and -3.006659276.

Subproblem 1
x + 2.8 = 3.006659276

Simplifying
x + 2.8 = 3.006659276

Reorder the terms:
2.8 + x = 3.006659276

Solving
2.8 + x = 3.006659276

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = 3.006659276 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = 3.006659276 + -2.8
x = 3.006659276 + -2.8

Combine like terms: 3.006659276 + -2.8 = 0.206659276
x = 0.206659276

Simplifying
x = 0.206659276

Subproblem 2
x + 2.8 = -3.006659276

Simplifying
x + 2.8 = -3.006659276

Reorder the terms:
2.8 + x = -3.006659276

Solving
2.8 + x = -3.006659276

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = -3.006659276 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = -3.006659276 + -2.8
x = -3.006659276 + -2.8

Combine like terms: -3.006659276 + -2.8 = -5.806659276
x = -5.806659276

Simplifying
x = -5.806659276

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.206659276, -5.806659276}
Solution
x = {0.206659276, -5.806659276}