X^2+256=64x

Solution for X^2+256=64x equation:

X^2+256=64X

We move all terms to the left:

X^2+256-(64X)=0

a = 1; b = -64; c = +256;
Δ = b2-4ac
Δ = -642-4·1·256
Δ = 3072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32\sqrt{3}}{2*1}=\frac{64-32\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{3}}{2*1}=\frac{64+32\sqrt{3}}{2}
$