X^2+y^2+12y+11=0

Solution for X^2+y^2+12y+11=0 equation:

X^2+X^2+12X+11=0

We add all the numbers together, and all the variables

2X^2+12X+11=0

a = 2; b = 12; c = +11;
Δ = b2-4ac
Δ = 122-4·2·11
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{14}}{2*2}=\frac{-12-2\sqrt{14}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{14}}{2*2}=\frac{-12+2\sqrt{14}}{4}
$