72^2+320^3=c^2

Solution for 72^2+320^3=c^2 equation:

72^2+320^3=c^2

We move all terms to the left:

72^2+320^3-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+32773184=0

a = -1; b = 0; c = +32773184;
Δ = b2-4ac
Δ = 02-4·(-1)·32773184
Δ = 131092736
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:

$\sqrt{\Delta}=\sqrt{131092736}=\sqrt{256*512081}=\sqrt{256}*\sqrt{512081}=16\sqrt{512081}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{512081}}{2*-1}=\frac{0-16\sqrt{512081}}{-2}
=-\frac{16\sqrt{512081}}{-2}
=-\frac{8\sqrt{512081}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{512081}}{2*-1}=\frac{0+16\sqrt{512081}}{-2}
=\frac{16\sqrt{512081}}{-2}
=\frac{8\sqrt{512081}}{-1}
$