3n(n-8)-8n=0

Solution for 3n(n-8)-8n=0 equation:

3n(n-8)-8n=0

We add all the numbers together, and all the variables

-8n+3n(n-8)=0

We multiply parentheses

3n^2-8n-24n=0

We add all the numbers together, and all the variables

3n^2-32n=0

a = 3; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·3·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*3}=\frac{64}{6}
=10+2/3
$