8n(3n+8)=2

Solution for 8n(3n+8)=2 equation:

8n(3n+8)=2

We move all terms to the left:

8n(3n+8)-(2)=0

We multiply parentheses

24n^2+64n-2=0

a = 24; b = 64; c = -2;
Δ = b2-4ac
Δ = 642-4·24·(-2)
Δ = 4288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4288}=\sqrt{64*67}=\sqrt{64}*\sqrt{67}=8\sqrt{67}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{67}}{2*24}=\frac{-64-8\sqrt{67}}{48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{67}}{2*24}=\frac{-64+8\sqrt{67}}{48}
$