15=0.5(h^2-h)

Solution for 15=0.5(h^2-h) equation:

Simplifying
15 = 0.5(h2 + -1h)

Reorder the terms:
15 = 0.5(-1h + h2)
15 = (-1h * 0.5 + h2 * 0.5)
15 = (-0.5h + 0.5h2)

Solving
15 = -0.5h + 0.5h2

Solving for variable 'h'.

Reorder the terms:
15 + 0.5h + -0.5h2 = -0.5h + 0.5h + 0.5h2 + -0.5h2

Combine like terms: -0.5h + 0.5h = 0.0
15 + 0.5h + -0.5h2 = 0.0 + 0.5h2 + -0.5h2
15 + 0.5h + -0.5h2 = 0.5h2 + -0.5h2

Combine like terms: 0.5h2 + -0.5h2 = 0.0
15 + 0.5h + -0.5h2 = 0.0

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

Divide each side by '-0.5'.
-30 + -1h + h2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -1h + 30 + h2 = 0 + 30

Reorder the terms:
-30 + 30 + -1h + h2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1h + h2 = 0 + 30
-1h + h2 = 0 + 30

Combine like terms: 0 + 30 = 30
-1h + h2 = 30

The h term is -1h.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1h + 0.25 + h2 = 30 + 0.25

Reorder the terms:
0.25 + -1h + h2 = 30 + 0.25

Combine like terms: 30 + 0.25 = 30.25
0.25 + -1h + h2 = 30.25

Factor a perfect square on the left side:
(h + -0.5)(h + -0.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(h + -0.5) equal to 5.5 and -5.5.

Subproblem 1
h + -0.5 = 5.5

Simplifying
h + -0.5 = 5.5

Reorder the terms:
-0.5 + h = 5.5

Solving
-0.5 + h = 5.5

Solving for variable 'h'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + h = 5.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + h = 5.5 + 0.5
h = 5.5 + 0.5

Combine like terms: 5.5 + 0.5 = 6
h = 6

Simplifying
h = 6

Subproblem 2
h + -0.5 = -5.5

Simplifying
h + -0.5 = -5.5

Reorder the terms:
-0.5 + h = -5.5

Solving
-0.5 + h = -5.5

Solving for variable 'h'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + h = -5.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + h = -5.5 + 0.5
h = -5.5 + 0.5

Combine like terms: -5.5 + 0.5 = -5
h = -5

Simplifying
h = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {6, -5}