c^2=20^2+126^2

Solution for c^2=20^2+126^2 equation:

c^2=20^2+126^2

We move all terms to the left:

c^2-(20^2+126^2)=0

We add all the numbers together, and all the variables

c^2-16276=0

a = 1; b = 0; c = -16276;
Δ = b2-4ac
Δ = 02-4·1·(-16276)
Δ = 65104
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:

$\sqrt{\Delta}=\sqrt{65104}=\sqrt{16*4069}=\sqrt{16}*\sqrt{4069}=4\sqrt{4069}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{4069}}{2*1}=\frac{0-4\sqrt{4069}}{2}
=-\frac{4\sqrt{4069}}{2}
=-2\sqrt{4069}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{4069}}{2*1}=\frac{0+4\sqrt{4069}}{2}
=\frac{4\sqrt{4069}}{2}
=2\sqrt{4069}
$