X2+y2+4y-117=0

Solution for X2+y2+4y-117=0 equation:

X2+X2+4X-117=0

We add all the numbers together, and all the variables

2X^2+4X-117=0

a = 2; b = 4; c = -117;
Δ = b2-4ac
Δ = 42-4·2·(-117)
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{238}}{2*2}=\frac{-4-2\sqrt{238}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{238}}{2*2}=\frac{-4+2\sqrt{238}}{4}
$