X^2+y^2-16y+15=0

Solution for X^2+y^2-16y+15=0 equation:

X^2+X^2-16X+15=0

We add all the numbers together, and all the variables

2X^2-16X+15=0

a = 2; b = -16; c = +15;
Δ = b2-4ac
Δ = -162-4·2·15
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{34}}{2*2}=\frac{16-2\sqrt{34}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{34}}{2*2}=\frac{16+2\sqrt{34}}{4}
$