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

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

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

We multiply parentheses ..

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

We get rid of parentheses

5n^2-20n-8n+32=0

We add all the numbers together, and all the variables

5n^2-28n+32=0

a = 5; b = -28; c = +32;
Δ = b2-4ac
Δ = -282-4·5·32
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12}{2*5}=\frac{16}{10}
=1+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12}{2*5}=\frac{40}{10}
=4
$