33^2+56^2=c2

Solution for 33^2+56^2=c2 equation:

33^2+56^2=c2

We move all terms to the left:

33^2+56^2-(c2)=0

We add all the numbers together, and all the variables

-1c^2+4225=0

a = -1; b = 0; c = +4225;
Δ = b2-4ac
Δ = 02-4·(-1)·4225
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-130}{2*-1}=\frac{-130}{-2}
=+65
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+130}{2*-1}=\frac{130}{-2}
=-65
$