44=5h+h^2

Solution for 44=5h+h^2 equation:

44=5h+h^2

We move all terms to the left:

44-(5h+h^2)=0

We get rid of parentheses

-h^2-5h+44=0

We add all the numbers together, and all the variables

-1h^2-5h+44=0

a = -1; b = -5; c = +44;
Δ = b2-4ac
Δ = -52-4·(-1)·44
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{201}}{2*-1}=\frac{5-\sqrt{201}}{-2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{201}}{2*-1}=\frac{5+\sqrt{201}}{-2}
$