20=128x-16x^2

Solution for 20=128x-16x^2 equation:

Simplifying
20 = 128x + -16x2

Solving
20 = 128x + -16x2

Solving for variable 'x'.

Reorder the terms:
20 + -128x + 16x2 = 128x + -128x + -16x2 + 16x2

Combine like terms: 128x + -128x = 0
20 + -128x + 16x2 = 0 + -16x2 + 16x2
20 + -128x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
20 + -128x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -32x + 4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -32x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + -32x + 4x2 = 0

Solving
5 + -32x + 4x2 = 0

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

Divide each side by '4'.
1.25 + -8x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -8x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -8x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -8x + x2 = 0 + -1.25
-8x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-8x + x2 = -1.25

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -1.25 + 16

Reorder the terms:
16 + -8x + x2 = -1.25 + 16

Combine like terms: -1.25 + 16 = 14.75
16 + -8x + x2 = 14.75

Factor a perfect square on the left side:
(x + -4)(x + -4) = 14.75

Calculate the square root of the right side: 3.840572874

Break this problem into two subproblems by setting 
(x + -4) equal to 3.840572874 and -3.840572874.

Subproblem 1
x + -4 = 3.840572874

Simplifying
x + -4 = 3.840572874

Reorder the terms:
-4 + x = 3.840572874

Solving
-4 + x = 3.840572874

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.840572874 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.840572874 + 4
x = 3.840572874 + 4

Combine like terms: 3.840572874 + 4 = 7.840572874
x = 7.840572874

Simplifying
x = 7.840572874

Subproblem 2
x + -4 = -3.840572874

Simplifying
x + -4 = -3.840572874

Reorder the terms:
-4 + x = -3.840572874

Solving
-4 + x = -3.840572874

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.840572874 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.840572874 + 4
x = -3.840572874 + 4

Combine like terms: -3.840572874 + 4 = 0.159427126
x = 0.159427126

Simplifying
x = 0.159427126

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.840572874, 0.159427126}
Solution
x = {7.840572874, 0.159427126}