0=6+80x-16x^2

Solution for 0=6+80x-16x^2 equation:

Simplifying
0 = 6 + 80x + -16x2

Solving
0 = 6 + 80x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -80x + 16x2 = 6 + 80x + -16x2 + -6 + -80x + 16x2

Reorder the terms:
-6 + -80x + 16x2 = 6 + -6 + 80x + -80x + -16x2 + 16x2

Combine like terms: 6 + -6 = 0
-6 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2
-6 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2

Combine like terms: 80x + -80x = 0
-6 + -80x + 16x2 = 0 + -16x2 + 16x2
-6 + -80x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-6 + -80x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -40x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -40x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + -40x + 8x2 = 0

Solving
-3 + -40x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + -5x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -5x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -5x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -5x + x2 = 0 + 0.375
-5x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-5x + x2 = 0.375

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 0.375 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 0.375 + 6.25

Combine like terms: 0.375 + 6.25 = 6.625
6.25 + -5x + x2 = 6.625

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 6.625

Calculate the square root of the right side: 2.573907535

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.573907535 and -2.573907535.

Subproblem 1
x + -2.5 = 2.573907535

Simplifying
x + -2.5 = 2.573907535

Reorder the terms:
-2.5 + x = 2.573907535

Solving
-2.5 + x = 2.573907535

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.573907535 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.573907535 + 2.5
x = 2.573907535 + 2.5

Combine like terms: 2.573907535 + 2.5 = 5.073907535
x = 5.073907535

Simplifying
x = 5.073907535

Subproblem 2
x + -2.5 = -2.573907535

Simplifying
x + -2.5 = -2.573907535

Reorder the terms:
-2.5 + x = -2.573907535

Solving
-2.5 + x = -2.573907535

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.573907535 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.573907535 + 2.5
x = -2.573907535 + 2.5

Combine like terms: -2.573907535 + 2.5 = -0.073907535
x = -0.073907535

Simplifying
x = -0.073907535

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.073907535, -0.073907535}
Solution
x = {5.073907535, -0.073907535}