X^2+y^2-10y-9=0

Solution for X^2+y^2-10y-9=0 equation:

X^2+X^2-10X-9=0

We add all the numbers together, and all the variables

2X^2-10X-9=0

a = 2; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·2·(-9)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{43}}{2*2}=\frac{10-2\sqrt{43}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{43}}{2*2}=\frac{10+2\sqrt{43}}{4}
$