x^2+13^2=82^2

Solution for x^2+13^2=82^2 equation:

x^2+13^2=82^2

We move all terms to the left:

x^2+13^2-(82^2)=0

We add all the numbers together, and all the variables

x^2-6555=0

a = 1; b = 0; c = -6555;
Δ = b2-4ac
Δ = 02-4·1·(-6555)
Δ = 26220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{26220}=\sqrt{4*6555}=\sqrt{4}*\sqrt{6555}=2\sqrt{6555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6555}}{2*1}=\frac{0-2\sqrt{6555}}{2}
=-\frac{2\sqrt{6555}}{2}
=-\sqrt{6555}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6555}}{2*1}=\frac{0+2\sqrt{6555}}{2}
=\frac{2\sqrt{6555}}{2}
=\sqrt{6555}
$