3n^2+3n-1002=0

Solution for 3n^2+3n-1002=0 equation:

3n^2+3n-1002=0

a = 3; b = 3; c = -1002;
Δ = b2-4ac
Δ = 32-4·3·(-1002)
Δ = 12033
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:

$\sqrt{\Delta}=\sqrt{12033}=\sqrt{9*1337}=\sqrt{9}*\sqrt{1337}=3\sqrt{1337}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{1337}}{2*3}=\frac{-3-3\sqrt{1337}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{1337}}{2*3}=\frac{-3+3\sqrt{1337}}{6}
$