6n(3n+4)=0

Solution for 6n(3n+4)=0 equation:

6n(3n+4)=0

We multiply parentheses

18n^2+24n=0

a = 18; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·18·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*18}=\frac{-48}{36}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*18}=\frac{0}{36}
=0
$