80^2+18^2=c^2

Solution for 80^2+18^2=c^2 equation:

80^2+18^2=c^2

We move all terms to the left:

80^2+18^2-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+6724=0

a = -1; b = 0; c = +6724;
Δ = b2-4ac
Δ = 02-4·(-1)·6724
Δ = 26896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26896}=164$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-164}{2*-1}=\frac{-164}{-2}
=+82
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+164}{2*-1}=\frac{164}{-2}
=-82
$