54^2+72^2=c^2

Solution for 54^2+72^2=c^2 equation:

54^2+72^2=c^2

We move all terms to the left:

54^2+72^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+8100=0

a = -1; b = 0; c = +8100;
Δ = b2-4ac
Δ = 02-4·(-1)·8100
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180}{2*-1}=\frac{-180}{-2}
=+90
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180}{2*-1}=\frac{180}{-2}
=-90
$