X^2-32x-512=0

Solution for X^2-32x-512=0 equation:

X^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}
$