8n^2+112n=-384

Solution for 8n^2+112n=-384 equation:

8n^2+112n=-384

We move all terms to the left:

8n^2+112n-(-384)=0

We add all the numbers together, and all the variables

8n^2+112n+384=0

a = 8; b = 112; c = +384;
Δ = b2-4ac
Δ = 1122-4·8·384
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-16}{2*8}=\frac{-128}{16}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+16}{2*8}=\frac{-96}{16}
=-6
$