4n(6n+4)=0

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

4n(6n+4)=0

We multiply parentheses

24n^2+16n=0

a = 24; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·24·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*24}=\frac{-32}{48}
=-2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*24}=\frac{0}{48}
=0
$