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

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

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

We multiply parentheses ..

(+5n^2-40n-4n+32)=0

We get rid of parentheses

5n^2-40n-4n+32=0

We add all the numbers together, and all the variables

5n^2-44n+32=0

a = 5; b = -44; c = +32;
Δ = b2-4ac
Δ = -442-4·5·32
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-36}{2*5}=\frac{8}{10}
=4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+36}{2*5}=\frac{80}{10}
=8
$