256=n*n

Solution for 256=n*n equation:

256=n*n

We move all terms to the left:

256-(n*n)=0

We add all the numbers together, and all the variables

-(+n*n)+256=0

We get rid of parentheses

-n*n+256=0

Wy multiply elements

-1n^2+256=0

a = -1; b = 0; c = +256;
Δ = b2-4ac
Δ = 02-4·(-1)·256
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*-1}=\frac{-32}{-2}
=+16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*-1}=\frac{32}{-2}
=-16
$