3n(n+6)=0

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

3n(n+6)=0

We multiply parentheses

3n^2+18n=0

a = 3; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·3·0
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*3}=\frac{-36}{6}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*3}=\frac{0}{6}
=0
$