h^2+9h=90^2

Solution for h^2+9h=90^2 equation:

h^2+9h=90^2

We move all terms to the left:

h^2+9h-(90^2)=0

We add all the numbers together, and all the variables

h^2+9h-8100=0

a = 1; b = 9; c = -8100;
Δ = b2-4ac
Δ = 92-4·1·(-8100)
Δ = 32481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32481}=\sqrt{81*401}=\sqrt{81}*\sqrt{401}=9\sqrt{401}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{401}}{2*1}=\frac{-9-9\sqrt{401}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{401}}{2*1}=\frac{-9+9\sqrt{401}}{2}
$