664=4h^2-48h+80

Solution for 664=4h^2-48h+80 equation:

Simplifying
664 = 4h2 + -48h + 80

Reorder the terms:
664 = 80 + -48h + 4h2

Solving
664 = 80 + -48h + 4h2

Solving for variable 'h'.

Combine like terms: 664 + -80 = 584
584 + 48h + -4h2 = 80 + -48h + 4h2 + -80 + 48h + -4h2

Reorder the terms:
584 + 48h + -4h2 = 80 + -80 + -48h + 48h + 4h2 + -4h2

Combine like terms: 80 + -80 = 0
584 + 48h + -4h2 = 0 + -48h + 48h + 4h2 + -4h2
584 + 48h + -4h2 = -48h + 48h + 4h2 + -4h2

Combine like terms: -48h + 48h = 0
584 + 48h + -4h2 = 0 + 4h2 + -4h2
584 + 48h + -4h2 = 4h2 + -4h2

Combine like terms: 4h2 + -4h2 = 0
584 + 48h + -4h2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(146 + 12h + -1h2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(146 + 12h + -1h2)' equal to zero and attempt to solve:

Simplifying
146 + 12h + -1h2 = 0

Solving
146 + 12h + -1h2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-146 + -12h + h2 = 0

Move the constant term to the right:

Add '146' to each side of the equation.
-146 + -12h + 146 + h2 = 0 + 146

Reorder the terms:
-146 + 146 + -12h + h2 = 0 + 146

Combine like terms: -146 + 146 = 0
0 + -12h + h2 = 0 + 146
-12h + h2 = 0 + 146

Combine like terms: 0 + 146 = 146
-12h + h2 = 146

The h term is -12h.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12h + 36 + h2 = 146 + 36

Reorder the terms:
36 + -12h + h2 = 146 + 36

Combine like terms: 146 + 36 = 182
36 + -12h + h2 = 182

Factor a perfect square on the left side:
(h + -6)(h + -6) = 182

Calculate the square root of the right side: 13.490737563

Break this problem into two subproblems by setting 
(h + -6) equal to 13.490737563 and -13.490737563.

Subproblem 1
h + -6 = 13.490737563

Simplifying
h + -6 = 13.490737563

Reorder the terms:
-6 + h = 13.490737563

Solving
-6 + h = 13.490737563

Solving for variable 'h'.

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

Add '6' to each side of the equation.
-6 + 6 + h = 13.490737563 + 6

Combine like terms: -6 + 6 = 0
0 + h = 13.490737563 + 6
h = 13.490737563 + 6

Combine like terms: 13.490737563 + 6 = 19.490737563
h = 19.490737563

Simplifying
h = 19.490737563

Subproblem 2
h + -6 = -13.490737563

Simplifying
h + -6 = -13.490737563

Reorder the terms:
-6 + h = -13.490737563

Solving
-6 + h = -13.490737563

Solving for variable 'h'.

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

Add '6' to each side of the equation.
-6 + 6 + h = -13.490737563 + 6

Combine like terms: -6 + 6 = 0
0 + h = -13.490737563 + 6
h = -13.490737563 + 6

Combine like terms: -13.490737563 + 6 = -7.490737563
h = -7.490737563

Simplifying
h = -7.490737563

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {19.490737563, -7.490737563}
Solution
h = {19.490737563, -7.490737563}