2h^2+6h-1224=0

Solution for 2h^2+6h-1224=0 equation:

Simplifying
2h2 + 6h + -1224 = 0

Reorder the terms:
-1224 + 6h + 2h2 = 0

Solving
-1224 + 6h + 2h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-612 + 3h + h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-612 + 3h + h2)' equal to zero and attempt to solve:

Simplifying
-612 + 3h + h2 = 0

Solving
-612 + 3h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '612' to each side of the equation.
-612 + 3h + 612 + h2 = 0 + 612

Reorder the terms:
-612 + 612 + 3h + h2 = 0 + 612

Combine like terms: -612 + 612 = 0
0 + 3h + h2 = 0 + 612
3h + h2 = 0 + 612

Combine like terms: 0 + 612 = 612
3h + h2 = 612

The h term is 3h.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3h + 2.25 + h2 = 612 + 2.25

Reorder the terms:
2.25 + 3h + h2 = 612 + 2.25

Combine like terms: 612 + 2.25 = 614.25
2.25 + 3h + h2 = 614.25

Factor a perfect square on the left side:
(h + 1.5)(h + 1.5) = 614.25

Calculate the square root of the right side: 24.784067463

Break this problem into two subproblems by setting 
(h + 1.5) equal to 24.784067463 and -24.784067463.

Subproblem 1
h + 1.5 = 24.784067463

Simplifying
h + 1.5 = 24.784067463

Reorder the terms:
1.5 + h = 24.784067463

Solving
1.5 + h = 24.784067463

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = 24.784067463 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = 24.784067463 + -1.5
h = 24.784067463 + -1.5

Combine like terms: 24.784067463 + -1.5 = 23.284067463
h = 23.284067463

Simplifying
h = 23.284067463

Subproblem 2
h + 1.5 = -24.784067463

Simplifying
h + 1.5 = -24.784067463

Reorder the terms:
1.5 + h = -24.784067463

Solving
1.5 + h = -24.784067463

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = -24.784067463 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = -24.784067463 + -1.5
h = -24.784067463 + -1.5

Combine like terms: -24.784067463 + -1.5 = -26.284067463
h = -26.284067463

Simplifying
h = -26.284067463

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {23.284067463, -26.284067463}
Solution
h = {23.284067463, -26.284067463}