-4n(8n+2)=0

Solution for -4n(8n+2)=0 equation:

-4n(8n+2)=0

We multiply parentheses

-32n^2-8n=0

a = -32; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-32)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-32}=\frac{0}{-64}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-32}=\frac{16}{-64}
=-1/4
$