x^2=2^8

Solution for x^2=2^8 equation:

x^2=2^8

We move all terms to the left:

x^2-(2^8)=0

We add all the numbers together, and all the variables

x^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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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