8n(n+2)=24

Solution for 8n(n+2)=24 equation:

8n(n+2)=24

We move all terms to the left:

8n(n+2)-(24)=0

We multiply parentheses

8n^2+16n-24=0

a = 8; b = 16; c = -24;
Δ = b2-4ac
Δ = 162-4·8·(-24)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-32}{2*8}=\frac{-48}{16}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+32}{2*8}=\frac{16}{16}
=1
$