390^2+120^2=c^2

Solution for 390^2+120^2=c^2 equation:

390^2+120^2=c^2

We move all terms to the left:

390^2+120^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+166500=0

a = -1; b = 0; c = +166500;
Δ = b2-4ac
Δ = 02-4·(-1)·166500
Δ = 666000
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:

$\sqrt{\Delta}=\sqrt{666000}=\sqrt{3600*185}=\sqrt{3600}*\sqrt{185}=60\sqrt{185}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{185}}{2*-1}=\frac{0-60\sqrt{185}}{-2}
=-\frac{60\sqrt{185}}{-2}
=-\frac{30\sqrt{185}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{185}}{2*-1}=\frac{0+60\sqrt{185}}{-2}
=\frac{60\sqrt{185}}{-2}
=\frac{30\sqrt{185}}{-1}
$