X^2+y^2=2y+48

Solution for X^2+y^2=2y+48 equation:

X^2+X^2=2X+48

We move all terms to the left:

X^2+X^2-(2X+48)=0

We add all the numbers together, and all the variables

2X^2-(2X+48)=0

We get rid of parentheses

2X^2-2X-48=0

a = 2; b = -2; c = -48;
Δ = b2-4ac
Δ = -22-4·2·(-48)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{97}}{2*2}=\frac{2-2\sqrt{97}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{97}}{2*2}=\frac{2+2\sqrt{97}}{4}
$