y^2-32y=64

Solution for y^2-32y=64 equation:

y^2-32y=64

We move all terms to the left:

y^2-32y-(64)=0

a = 1; b = -32; c = -64;
Δ = b2-4ac
Δ = -322-4·1·(-64)
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{5}}{2*1}=\frac{32-16\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{5}}{2*1}=\frac{32+16\sqrt{5}}{2}
$