n^2+12n=-11

Solution for n^2+12n=-11 equation:

n^2+12n=-11

We move all terms to the left:

n^2+12n-(-11)=0

We add all the numbers together, and all the variables

n^2+12n+11=0

a = 1; b = 12; c = +11;
Δ = b2-4ac
Δ = 122-4·1·11
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10}{2*1}=\frac{-22}{2}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10}{2*1}=\frac{-2}{2}
=-1
$