4h^2+18h-26=0

Solution for 4h^2+18h-26=0 equation:

Simplifying
4h2 + 18h + -26 = 0

Reorder the terms:
-26 + 18h + 4h2 = 0

Solving
-26 + 18h + 4h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 9h + 2h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 9h + 2h2)' equal to zero and attempt to solve:

Simplifying
-13 + 9h + 2h2 = 0

Solving
-13 + 9h + 2h2 = 0

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

Divide each side by '2'.
-6.5 + 4.5h + h2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 4.5h + 6.5 + h2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 4.5h + h2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 4.5h + h2 = 0 + 6.5
4.5h + h2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
4.5h + h2 = 6.5

The h term is 4.5h.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5h + 5.0625 + h2 = 6.5 + 5.0625

Reorder the terms:
5.0625 + 4.5h + h2 = 6.5 + 5.0625

Combine like terms: 6.5 + 5.0625 = 11.5625
5.0625 + 4.5h + h2 = 11.5625

Factor a perfect square on the left side:
(h + 2.25)(h + 2.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(h + 2.25) equal to 3.400367627 and -3.400367627.

Subproblem 1
h + 2.25 = 3.400367627

Simplifying
h + 2.25 = 3.400367627

Reorder the terms:
2.25 + h = 3.400367627

Solving
2.25 + h = 3.400367627

Solving for variable 'h'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + h = 3.400367627 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + h = 3.400367627 + -2.25
h = 3.400367627 + -2.25

Combine like terms: 3.400367627 + -2.25 = 1.150367627
h = 1.150367627

Simplifying
h = 1.150367627

Subproblem 2
h + 2.25 = -3.400367627

Simplifying
h + 2.25 = -3.400367627

Reorder the terms:
2.25 + h = -3.400367627

Solving
2.25 + h = -3.400367627

Solving for variable 'h'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + h = -3.400367627 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + h = -3.400367627 + -2.25
h = -3.400367627 + -2.25

Combine like terms: -3.400367627 + -2.25 = -5.650367627
h = -5.650367627

Simplifying
h = -5.650367627

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.150367627, -5.650367627}
Solution
h = {1.150367627, -5.650367627}