8=-4n2-12n

Solution for 8=-4n2-12n equation:

8=-4n^2-12n

We move all terms to the left:

8-(-4n^2-12n)=0

We get rid of parentheses

4n^2+12n+8=0

a = 4; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·4·8
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4}{2*4}=\frac{-16}{8}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4}{2*4}=\frac{-8}{8}
=-1
$