X2+y2+6y+2=0

Solution for X2+y2+6y+2=0 equation:

X2+X2+6X+2=0

We add all the numbers together, and all the variables

2X^2+6X+2=0

a = 2; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·2·2
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*2}=\frac{-6-2\sqrt{5}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*2}=\frac{-6+2\sqrt{5}}{4}
$