X^2+y^2-6y-55=0

Solution for X^2+y^2-6y-55=0 equation:

X^2+X^2-6X-55=0

We add all the numbers together, and all the variables

2X^2-6X-55=0

a = 2; b = -6; c = -55;
Δ = b2-4ac
Δ = -62-4·2·(-55)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{119}}{2*2}=\frac{6-2\sqrt{119}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{119}}{2*2}=\frac{6+2\sqrt{119}}{4}
$