X^2+y2+8y=33

Solution for X^2+y2+8y=33 equation:

X^2+X2+8X=33

We move all terms to the left:

X^2+X2+8X-(33)=0

We add all the numbers together, and all the variables

2X^2+8X-33=0

a = 2; b = 8; c = -33;
Δ = b2-4ac
Δ = 82-4·2·(-33)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{82}}{2*2}=\frac{-8-2\sqrt{82}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{82}}{2*2}=\frac{-8+2\sqrt{82}}{4}
$