-8n^2-12n=0

Solution for -8n^2-12n=0 equation:

-8n^2-12n=0

a = -8; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-8)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-8}=\frac{0}{-16}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-8}=\frac{24}{-16}
=-1+1/2
$