3n^2+37n-1638=0.

Solution for 3n^2+37n-1638=0. equation:

3n^2+37n-1638=0.

a = 3; b = 37; c = -1638;
Δ = b2-4ac
Δ = 372-4·3·(-1638)
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-145}{2*3}=\frac{-182}{6}
=-30+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+145}{2*3}=\frac{108}{6}
=18
$