2(n-9)(n-12)=0

Solution for 2(n-9)(n-12)=0 equation:

2(n-9)(n-12)=0

We multiply parentheses ..

2(+n^2-12n-9n+108)=0

We multiply parentheses

2n^2-24n-18n+216=0

We add all the numbers together, and all the variables

2n^2-42n+216=0

a = 2; b = -42; c = +216;
Δ = b2-4ac
Δ = -422-4·2·216
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6}{2*2}=\frac{36}{4}
=9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6}{2*2}=\frac{48}{4}
=12
$