X2+y2+8y-84=0

Solution for X2+y2+8y-84=0 equation:

X2+X2+8X-84=0

We add all the numbers together, and all the variables

2X^2+8X-84=0

a = 2; b = 8; c = -84;
Δ = b2-4ac
Δ = 82-4·2·(-84)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{46}}{2*2}=\frac{-8-4\sqrt{46}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{46}}{2*2}=\frac{-8+4\sqrt{46}}{4}
$