192^2+256^2=c^2

Solution for 192^2+256^2=c^2 equation:

192^2+256^2=c^2

We move all terms to the left:

192^2+256^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+102400=0

a = -1; b = 0; c = +102400;
Δ = b2-4ac
Δ = 02-4·(-1)·102400
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-640}{2*-1}=\frac{-640}{-2}
=+320
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+640}{2*-1}=\frac{640}{-2}
=-320
$