24^2+45^2=c^2

Solution for 24^2+45^2=c^2 equation:

24^2+45^2=c^2

We move all terms to the left:

24^2+45^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+2601=0

a = -1; b = 0; c = +2601;
Δ = b2-4ac
Δ = 02-4·(-1)·2601
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-102}{2*-1}=\frac{-102}{-2}
=+51
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+102}{2*-1}=\frac{102}{-2}
=-51
$