0=x^2-64x+512

Solution for 0=x^2-64x+512 equation:

0=x^2-64x+512

We move all terms to the left:

0-(x^2-64x+512)=0

We add all the numbers together, and all the variables

-(x^2-64x+512)=0

We get rid of parentheses

-x^2+64x-512=0

We add all the numbers together, and all the variables

-1x^2+64x-512=0

a = -1; b = 64; c = -512;
Δ = b2-4ac
Δ = 642-4·(-1)·(-512)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-32\sqrt{2}}{2*-1}=\frac{-64-32\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+32\sqrt{2}}{2*-1}=\frac{-64+32\sqrt{2}}{-2}
$