20=6+31x-16x^2

Solution for 20=6+31x-16x^2 equation:

Simplifying
20 = 6 + 31x + -16x2

Solving
20 = 6 + 31x + -16x2

Solving for variable 'x'.

Combine like terms: 20 + -6 = 14
14 + -31x + 16x2 = 6 + 31x + -16x2 + -6 + -31x + 16x2

Reorder the terms:
14 + -31x + 16x2 = 6 + -6 + 31x + -31x + -16x2 + 16x2

Combine like terms: 6 + -6 = 0
14 + -31x + 16x2 = 0 + 31x + -31x + -16x2 + 16x2
14 + -31x + 16x2 = 31x + -31x + -16x2 + 16x2

Combine like terms: 31x + -31x = 0
14 + -31x + 16x2 = 0 + -16x2 + 16x2
14 + -31x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
14 + -31x + 16x2 = 0

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

Divide each side by '16'.
0.875 + -1.9375x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + -1.9375x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + -1.9375x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + -1.9375x + x2 = 0 + -0.875
-1.9375x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
-1.9375x + x2 = -0.875

The x term is -1.9375x.  Take half its coefficient (-0.96875).
Square it (0.9384765625) and add it to both sides.

Add '0.9384765625' to each side of the equation.
-1.9375x + 0.9384765625 + x2 = -0.875 + 0.9384765625

Reorder the terms:
0.9384765625 + -1.9375x + x2 = -0.875 + 0.9384765625

Combine like terms: -0.875 + 0.9384765625 = 0.0634765625
0.9384765625 + -1.9375x + x2 = 0.0634765625

Factor a perfect square on the left side:
(x + -0.96875)(x + -0.96875) = 0.0634765625

Calculate the square root of the right side: 0.251945555

Break this problem into two subproblems by setting 
(x + -0.96875) equal to 0.251945555 and -0.251945555.

Subproblem 1
x + -0.96875 = 0.251945555

Simplifying
x + -0.96875 = 0.251945555

Reorder the terms:
-0.96875 + x = 0.251945555

Solving
-0.96875 + x = 0.251945555

Solving for variable 'x'.

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

Add '0.96875' to each side of the equation.
-0.96875 + 0.96875 + x = 0.251945555 + 0.96875

Combine like terms: -0.96875 + 0.96875 = 0.00000
0.00000 + x = 0.251945555 + 0.96875
x = 0.251945555 + 0.96875

Combine like terms: 0.251945555 + 0.96875 = 1.220695555
x = 1.220695555

Simplifying
x = 1.220695555

Subproblem 2
x + -0.96875 = -0.251945555

Simplifying
x + -0.96875 = -0.251945555

Reorder the terms:
-0.96875 + x = -0.251945555

Solving
-0.96875 + x = -0.251945555

Solving for variable 'x'.

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

Add '0.96875' to each side of the equation.
-0.96875 + 0.96875 + x = -0.251945555 + 0.96875

Combine like terms: -0.96875 + 0.96875 = 0.00000
0.00000 + x = -0.251945555 + 0.96875
x = -0.251945555 + 0.96875

Combine like terms: -0.251945555 + 0.96875 = 0.716804445
x = 0.716804445

Simplifying
x = 0.716804445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.220695555, 0.716804445}