1026=111n-3n^2

Solution for 1026=111n-3n^2 equation:

1026=111n-3n^2

We move all terms to the left:

1026-(111n-3n^2)=0

We get rid of parentheses

3n^2-111n+1026=0

a = 3; b = -111; c = +1026;
Δ = b2-4ac
Δ = -1112-4·3·1026
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-3}{2*3}=\frac{108}{6}
=18
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+3}{2*3}=\frac{114}{6}
=19
$