3n^2+303n-16200=0

Solution for 3n^2+303n-16200=0 equation:

3n^2+303n-16200=0

a = 3; b = 303; c = -16200;
Δ = b2-4ac
Δ = 3032-4·3·(-16200)
Δ = 286209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{286209}=\sqrt{441*649}=\sqrt{441}*\sqrt{649}=21\sqrt{649}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(303)-21\sqrt{649}}{2*3}=\frac{-303-21\sqrt{649}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(303)+21\sqrt{649}}{2*3}=\frac{-303+21\sqrt{649}}{6}
$