6(8n-5)(n-4)=0

Solution for 6(8n-5)(n-4)=0 equation:

6(8n-5)(n-4)=0

We multiply parentheses ..

6(+8n^2-32n-5n+20)=0

We multiply parentheses

48n^2-192n-30n+120=0

We add all the numbers together, and all the variables

48n^2-222n+120=0

a = 48; b = -222; c = +120;
Δ = b2-4ac
Δ = -2222-4·48·120
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-222)-162}{2*48}=\frac{60}{96}
=5/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-222)+162}{2*48}=\frac{384}{96}
=4
$