33^2+h^2=65^2

Solution for 33^2+h^2=65^2 equation:

33^2+h^2=65^2

We move all terms to the left:

33^2+h^2-(65^2)=0

We add all the numbers together, and all the variables

h^2-3136=0

a = 1; b = 0; c = -3136;
Δ = b2-4ac
Δ = 02-4·1·(-3136)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112}{2*1}=\frac{-112}{2}
=-56
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112}{2*1}=\frac{112}{2}
=56
$