X2+y2-4y-45=0

Solution for X2+y2-4y-45=0 equation:

X2+X2-4X-45=0

We add all the numbers together, and all the variables

2X^2-4X-45=0

a = 2; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·2·(-45)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*2}=\frac{4-2\sqrt{94}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*2}=\frac{4+2\sqrt{94}}{4}
$