5x^2-16x=-x^2+80

Solution for 5x^2-16x=-x^2+80 equation:

Simplifying
5x2 + -16x = -1x2 + 80

Reorder the terms:
-16x + 5x2 = -1x2 + 80

Reorder the terms:
-16x + 5x2 = 80 + -1x2

Solving
-16x + 5x2 = 80 + -1x2

Solving for variable 'x'.

Reorder the terms:
-80 + -16x + 5x2 + x2 = 80 + -1x2 + -80 + x2

Combine like terms: 5x2 + x2 = 6x2
-80 + -16x + 6x2 = 80 + -1x2 + -80 + x2

Reorder the terms:
-80 + -16x + 6x2 = 80 + -80 + -1x2 + x2

Combine like terms: 80 + -80 = 0
-80 + -16x + 6x2 = 0 + -1x2 + x2
-80 + -16x + 6x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-80 + -16x + 6x2 = 0

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

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

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

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

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

Divide each side by '3'.
-13.33333333 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -2.666666667x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -2.666666667x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 13.33333333
-2.666666667x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-2.666666667x + x2 = 13.33333333

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 13.33333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 13.33333333 + 1.777777780

Combine like terms: 13.33333333 + 1.777777780 = 15.11111111
1.777777780 + -2.666666667x + x2 = 15.11111111

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 15.11111111

Calculate the square root of the right side: 3.887301263

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 3.887301263 and -3.887301263.

Subproblem 1
x + -1.333333334 = 3.887301263

Simplifying
x + -1.333333334 = 3.887301263

Reorder the terms:
-1.333333334 + x = 3.887301263

Solving
-1.333333334 + x = 3.887301263

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 3.887301263 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 3.887301263 + 1.333333334
x = 3.887301263 + 1.333333334

Combine like terms: 3.887301263 + 1.333333334 = 5.220634597
x = 5.220634597

Simplifying
x = 5.220634597

Subproblem 2
x + -1.333333334 = -3.887301263

Simplifying
x + -1.333333334 = -3.887301263

Reorder the terms:
-1.333333334 + x = -3.887301263

Solving
-1.333333334 + x = -3.887301263

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -3.887301263 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -3.887301263 + 1.333333334
x = -3.887301263 + 1.333333334

Combine like terms: -3.887301263 + 1.333333334 = -2.553967929
x = -2.553967929

Simplifying
x = -2.553967929

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.220634597, -2.553967929}
Solution
x = {5.220634597, -2.553967929}