3n^2+6n=1005

Solution for 3n^2+6n=1005 equation:

3n^2+6n=1005

We move all terms to the left:

3n^2+6n-(1005)=0

a = 3; b = 6; c = -1005;
Δ = b2-4ac
Δ = 62-4·3·(-1005)
Δ = 12096
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:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24\sqrt{21}}{2*3}=\frac{-6-24\sqrt{21}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24\sqrt{21}}{2*3}=\frac{-6+24\sqrt{21}}{6}
$