y^2=8y+16=64

Solution for y^2=8y+16=64 equation:

y^2=8y+16=64

We move all terms to the left:

y^2-(8y+16)=0

We get rid of parentheses

y^2-8y-16=0

a = 1; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·1·(-16)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{2}}{2*1}=\frac{8-8\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{2}}{2*1}=\frac{8+8\sqrt{2}}{2}
$