11n-n^2=24

Solution for 11n-n^2=24 equation:

11n-n^2=24

We move all terms to the left:

11n-n^2-(24)=0

We add all the numbers together, and all the variables

-1n^2+11n-24=0

a = -1; b = 11; c = -24;
Δ = b2-4ac
Δ = 112-4·(-1)·(-24)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*-1}=\frac{-16}{-2}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-1}=\frac{-6}{-2}
=+3
$