24^2+8^2=c^2

Solution for 24^2+8^2=c^2 equation:

24^2+8^2=c^2

We move all terms to the left:

24^2+8^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+640=0

a = -1; b = 0; c = +640;
Δ = b2-4ac
Δ = 02-4·(-1)·640
Δ = 2560
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{10}}{2*-1}=\frac{0-16\sqrt{10}}{-2}
=-\frac{16\sqrt{10}}{-2}
=-\frac{8\sqrt{10}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{10}}{2*-1}=\frac{0+16\sqrt{10}}{-2}
=\frac{16\sqrt{10}}{-2}
=\frac{8\sqrt{10}}{-1}
$