512+32x=x^2

Solution for 512+32x=x^2 equation:

512+32x=x^2

We move all terms to the left:

512+32x-(x^2)=0

determiningTheFunctionDomain
-x^2+32x+512=0

We add all the numbers together, and all the variables

-1x^2+32x+512=0

a = -1; b = 32; c = +512;
Δ = b2-4ac
Δ = 322-4·(-1)·512
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{-(32)-32\sqrt{3}}{2*-1}=\frac{-32-32\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32\sqrt{3}}{2*-1}=\frac{-32+32\sqrt{3}}{-2}
$