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

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

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

We multiply parentheses ..

5(+n^2-8n-4n+32)=0

We multiply parentheses

5n^2-40n-20n+160=0

We add all the numbers together, and all the variables

5n^2-60n+160=0

a = 5; b = -60; c = +160;
Δ = b2-4ac
Δ = -602-4·5·160
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20}{2*5}=\frac{40}{10}
=4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20}{2*5}=\frac{80}{10}
=8
$