Y=n^2+11n+24

Solution for Y=n^2+11n+24 equation:

=Y^2+11Y+24

We move all terms to the left:

-(Y^2+11Y+24)=0

We get rid of parentheses

-Y^2-11Y-24=0

We add all the numbers together, and all the variables

-1Y^2-11Y-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:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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