12=3n^2+16n

Solution for 12=3n^2+16n equation:

12=3n^2+16n

We move all terms to the left:

12-(3n^2+16n)=0

We get rid of parentheses

-3n^2-16n+12=0

a = -3; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·(-3)·12
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20}{2*-3}=\frac{-4}{-6}
=2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*-3}=\frac{36}{-6}
=-6
$