21^2+72^2=c^2

Solution for 21^2+72^2=c^2 equation:

21^2+72^2=c^2

We move all terms to the left:

21^2+72^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+5625=0

a = -1; b = 0; c = +5625;
Δ = b2-4ac
Δ = 02-4·(-1)·5625
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150}{2*-1}=\frac{-150}{-2}
=+75
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150}{2*-1}=\frac{150}{-2}
=-75
$