0.5h^2+3h-36=0

Solution for 0.5h^2+3h-36=0 equation:

Simplifying
0.5h2 + 3h + -36 = 0

Reorder the terms:
-36 + 3h + 0.5h2 = 0

Solving
-36 + 3h + 0.5h2 = 0

Solving for variable 'h'.

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

Divide each side by '0.5'.
-72 + 6h + h2 = 0

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 6h + 72 + h2 = 0 + 72

Reorder the terms:
-72 + 72 + 6h + h2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 6h + h2 = 0 + 72
6h + h2 = 0 + 72

Combine like terms: 0 + 72 = 72
6h + h2 = 72

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 = 72 + 9

Reorder the terms:
9 + 6h + h2 = 72 + 9

Combine like terms: 72 + 9 = 81
9 + 6h + h2 = 81

Factor a perfect square on the left side:
(h + 3)(h + 3) = 81

Calculate the square root of the right side: 9

Break this problem into two subproblems by setting 
(h + 3) equal to 9 and -9.

Subproblem 1
h + 3 = 9

Simplifying
h + 3 = 9

Reorder the terms:
3 + h = 9

Solving
3 + h = 9

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 = 9 + -3

Combine like terms: 3 + -3 = 0
0 + h = 9 + -3
h = 9 + -3

Combine like terms: 9 + -3 = 6
h = 6

Simplifying
h = 6

Subproblem 2
h + 3 = -9

Simplifying
h + 3 = -9

Reorder the terms:
3 + h = -9

Solving
3 + h = -9

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 = -9 + -3

Combine like terms: 3 + -3 = 0
0 + h = -9 + -3
h = -9 + -3

Combine like terms: -9 + -3 = -12
h = -12

Simplifying
h = -12

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {6, -12}