X^2+y^2+8y-24=0

Solution for X^2+y^2+8y-24=0 equation:

X^2+X^2+8X-24=0

We add all the numbers together, and all the variables

2X^2+8X-24=0

a = 2; b = 8; c = -24;
Δ = b2-4ac
Δ = 82-4·2·(-24)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*2}=\frac{-24}{4}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*2}=\frac{8}{4}
=2
$