-11n=-2n^2+21

Solution for -11n=-2n^2+21 equation:

-11n=-2n^2+21

We move all terms to the left:

-11n-(-2n^2+21)=0

We get rid of parentheses

2n^2-11n-21=0

a = 2; b = -11; c = -21;
Δ = b2-4ac
Δ = -112-4·2·(-21)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*2}=\frac{-6}{4}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*2}=\frac{28}{4}
=7
$