8n^2+56n=-96

Solution for 8n^2+56n=-96 equation:

8n^2+56n=-96

We move all terms to the left:

8n^2+56n-(-96)=0

We add all the numbers together, and all the variables

8n^2+56n+96=0

a = 8; b = 56; c = +96;
Δ = b2-4ac
Δ = 562-4·8·96
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{-(56)-8}{2*8}=\frac{-64}{16}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8}{2*8}=\frac{-48}{16}
=-3
$