2^16=n^2

Solution for 2^16=n^2 equation:

2^16=n^2

We move all terms to the left:

2^16-(n^2)=0

We add all the numbers together, and all the variables

-1n^2+65536=0

a = -1; b = 0; c = +65536;
Δ = b2-4ac
Δ = 02-4·(-1)·65536
Δ = 262144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{262144}=512$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-512}{2*-1}=\frac{-512}{-2}
=+256
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+512}{2*-1}=\frac{512}{-2}
=-256
$