X^2+y^2-8y=8

Solution for X^2+y^2-8y=8 equation:

X^2+X^2-8X=8

We move all terms to the left:

X^2+X^2-8X-(8)=0

We add all the numbers together, and all the variables

2X^2-8X-8=0

a = 2; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·2·(-8)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{2}}{2*2}=\frac{8-8\sqrt{2}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{2}}{2*2}=\frac{8+8\sqrt{2}}{4}
$