3n^2+17n-1000=0

Solution for 3n^2+17n-1000=0 equation:

3n^2+17n-1000=0

a = 3; b = 17; c = -1000;
Δ = b2-4ac
Δ = 172-4·3·(-1000)
Δ = 12289
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{-(17)-\sqrt{12289}}{2*3}=\frac{-17-\sqrt{12289}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{12289}}{2*3}=\frac{-17+\sqrt{12289}}{6}
$