9^2+40^2=c^2

Solution for 9^2+40^2=c^2 equation:

9^2+40^2=c^2

We move all terms to the left:

9^2+40^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+1681=0

a = -1; b = 0; c = +1681;
Δ = b2-4ac
Δ = 02-4·(-1)·1681
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-82}{2*-1}=\frac{-82}{-2}
=+41
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+82}{2*-1}=\frac{82}{-2}
=-41
$