3n^2+37n-2000=0

Solution for 3n^2+37n-2000=0 equation:

3n^2+37n-2000=0

a = 3; b = 37; c = -2000;
Δ = b2-4ac
Δ = 372-4·3·(-2000)
Δ = 25369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-\sqrt{25369}}{2*3}=\frac{-37-\sqrt{25369}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{25369}}{2*3}=\frac{-37+\sqrt{25369}}{6}
$