a^2+18^2=82^2

Solution for a^2+18^2=82^2 equation:

a^2+18^2=82^2

We move all terms to the left:

a^2+18^2-(82^2)=0

We add all the numbers together, and all the variables

a^2-6400=0

a = 1; b = 0; c = -6400;
Δ = b2-4ac
Δ = 02-4·1·(-6400)
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160}{2*1}=\frac{-160}{2}
=-80
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160}{2*1}=\frac{160}{2}
=80
$