x^2=512-16x

Solution for x^2=512-16x equation:

x^2=512-16x

We move all terms to the left:

x^2-(512-16x)=0

We add all the numbers together, and all the variables

x^2-(-16x+512)=0

We get rid of parentheses

x^2+16x-512=0

a = 1; b = 16; c = -512;
Δ = b2-4ac
Δ = 162-4·1·(-512)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-48}{2*1}=\frac{-64}{2}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+48}{2*1}=\frac{32}{2}
=16
$