n^2+11n=-10

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

n^2+11n=-10

We move all terms to the left:

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

We add all the numbers together, and all the variables

n^2+11n+10=0

a = 1; b = 11; c = +10;
Δ = b2-4ac
Δ = 112-4·1·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*1}=\frac{-20}{2}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*1}=\frac{-2}{2}
=-1
$