5n(8n+1)=0

Solution for 5n(8n+1)=0 equation:

5n(8n+1)=0

We multiply parentheses

40n^2+5n=0

a = 40; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·40·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*40}=\frac{-10}{80}
=-1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*40}=\frac{0}{80}
=0
$