8n+12n(6n-4)=0

Solution for 8n+12n(6n-4)=0 equation:

8n+12n(6n-4)=0

We multiply parentheses

72n^2+8n-48n=0

We add all the numbers together, and all the variables

72n^2-40n=0

a = 72; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·72·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*72}=\frac{0}{144}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*72}=\frac{80}{144}
=5/9
$