5n(4n+5)=0

Solution for 5n(4n+5)=0 equation:

5n(4n+5)=0

We multiply parentheses

20n^2+25n=0

a = 20; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·20·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*20}=\frac{-50}{40}
=-1+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*20}=\frac{0}{40}
=0
$