h^2+4=6h

Solution for h^2+4=6h equation:

Simplifying
h2 + 4 = 6h

Reorder the terms:
4 + h2 = 6h

Solving
4 + h2 = 6h

Solving for variable 'h'.

Reorder the terms:
4 + -6h + h2 = 6h + -6h

Combine like terms: 6h + -6h = 0
4 + -6h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6h + -4 + h2 = 0 + -4

Reorder the terms:
4 + -4 + -6h + h2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6h + h2 = 0 + -4
-6h + h2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6h + h2 = -4

The h term is -6h.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6h + 9 + h2 = -4 + 9

Reorder the terms:
9 + -6h + h2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6h + h2 = 5

Factor a perfect square on the left side:
(h + -3)(h + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(h + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1
h + -3 = 2.236067978

Simplifying
h + -3 = 2.236067978

Reorder the terms:
-3 + h = 2.236067978

Solving
-3 + h = 2.236067978

Solving for variable 'h'.

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

Add '3' to each side of the equation.
-3 + 3 + h = 2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + h = 2.236067978 + 3
h = 2.236067978 + 3

Combine like terms: 2.236067978 + 3 = 5.236067978
h = 5.236067978

Simplifying
h = 5.236067978

Subproblem 2
h + -3 = -2.236067978

Simplifying
h + -3 = -2.236067978

Reorder the terms:
-3 + h = -2.236067978

Solving
-3 + h = -2.236067978

Solving for variable 'h'.

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

Add '3' to each side of the equation.
-3 + 3 + h = -2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + h = -2.236067978 + 3
h = -2.236067978 + 3

Combine like terms: -2.236067978 + 3 = 0.763932022
h = 0.763932022

Simplifying
h = 0.763932022

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {5.236067978, 0.763932022}