y^2+10y=-11

Solution for y^2+10y=-11 equation:

y^2+10y=-11

We move all terms to the left:

y^2+10y-(-11)=0

We add all the numbers together, and all the variables

y^2+10y+11=0

a = 1; b = 10; c = +11;
Δ = b2-4ac
Δ = 102-4·1·11
Δ = 56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{14}}{2*1}=\frac{-10-2\sqrt{14}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{14}}{2*1}=\frac{-10+2\sqrt{14}}{2}
$