-4n(3n+5)=0

Solution for -4n(3n+5)=0 equation:

-4n(3n+5)=0

We multiply parentheses

-12n^2-20n=0

a = -12; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-12)·0
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{-(-20)-20}{2*-12}=\frac{0}{-24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-12}=\frac{40}{-24}
=-1+2/3
$