24^2+32^2=c^2

Solution for 24^2+32^2=c^2 equation:

24^2+32^2=c^2

We move all terms to the left:

24^2+32^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+1600=0

a = -1; b = 0; c = +1600;
Δ = b2-4ac
Δ = 02-4·(-1)·1600
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*-1}=\frac{-80}{-2}
=+40
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*-1}=\frac{80}{-2}
=-40
$