5n(2n-5)=0

Solution for 5n(2n-5)=0 equation:

5n(2n-5)=0

We multiply parentheses

10n^2-25n=0

a = 10; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·10·0
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*10}=\frac{0}{20}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*10}=\frac{50}{20}
=2+1/2
$