1.5n^2+18.5n-680=0

Solution for 1.5n^2+18.5n-680=0 equation:

1.5n^2+18.5n-680=0

a = 1.5; b = 18.5; c = -680;
Δ = b2-4ac
Δ = 18.52-4·1.5·(-680)
Δ = 4422.25
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{-(18.5)-\sqrt{4422.25}}{2*1.5}=\frac{-18.5-\sqrt{4422.25}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18.5)+\sqrt{4422.25}}{2*1.5}=\frac{-18.5+\sqrt{4422.25}}{3}
$