-11n+10=-n^2

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

-11n+10=-n^2

We move all terms to the left:

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

We get rid of parentheses

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