X^2+y^2-16y-36=0

Solution for X^2+y^2-16y-36=0 equation:

X^2+X^2-16X-36=0

We add all the numbers together, and all the variables

2X^2-16X-36=0

a = 2; b = -16; c = -36;
Δ = b2-4ac
Δ = -162-4·2·(-36)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{34}}{2*2}=\frac{16-4\sqrt{34}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{34}}{2*2}=\frac{16+4\sqrt{34}}{4}
$