5x^2=x^2+256

Solution for 5x^2=x^2+256 equation:

5x^2=x^2+256

We move all terms to the left:

5x^2-(x^2+256)=0

We get rid of parentheses

5x^2-x^2-256=0

We add all the numbers together, and all the variables

4x^2-256=0

a = 4; b = 0; c = -256;
Δ = b2-4ac
Δ = 02-4·4·(-256)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*4}=\frac{64}{8}
=8
$