3n(2n+6)=0

Solution for 3n(2n+6)=0 equation:

3n(2n+6)=0

We multiply parentheses

6n^2+18n=0

a = 6; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·6·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*6}=\frac{-36}{12}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*6}=\frac{0}{12}
=0
$