2g^2-4g=20

Solution for 2g^2-4g=20 equation:

Simplifying
2g2 + -4g = 20

Reorder the terms:
-4g + 2g2 = 20

Solving
-4g + 2g2 = 20

Solving for variable 'g'.

Reorder the terms:
-20 + -4g + 2g2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -4g + 2g2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -2g + g2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -2g + g2)' equal to zero and attempt to solve:

Simplifying
-10 + -2g + g2 = 0

Solving
-10 + -2g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2g + 10 + g2 = 0 + 10

Reorder the terms:
-10 + 10 + -2g + g2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2g + g2 = 0 + 10
-2g + g2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2g + g2 = 10

The g term is -2g.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2g + 1 + g2 = 10 + 1

Reorder the terms:
1 + -2g + g2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2g + g2 = 11

Factor a perfect square on the left side:
(g + -1)(g + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(g + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1
g + -1 = 3.31662479

Simplifying
g + -1 = 3.31662479

Reorder the terms:
-1 + g = 3.31662479

Solving
-1 + g = 3.31662479

Solving for variable 'g'.

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

Add '1' to each side of the equation.
-1 + 1 + g = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + g = 3.31662479 + 1
g = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
g = 4.31662479

Simplifying
g = 4.31662479

Subproblem 2
g + -1 = -3.31662479

Simplifying
g + -1 = -3.31662479

Reorder the terms:
-1 + g = -3.31662479

Solving
-1 + g = -3.31662479

Solving for variable 'g'.

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

Add '1' to each side of the equation.
-1 + 1 + g = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + g = -3.31662479 + 1
g = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
g = -2.31662479

Simplifying
g = -2.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {4.31662479, -2.31662479}
Solution
g = {4.31662479, -2.31662479}