How to isolate $n$ in the inequality $ 3n + 7n^3\gt c(17 + 34n^2) $? I have an equation 
$$ 3n + 7n^3\gt c\left(17 + 34n^2\right)
$$
and I want to turn this inequality into something like 
$$ n \gt c(\mbox{something that does not have}\ n)
$$
I don't know why but always get stumped at these types of questions. Any help would be appreciated, thanks.

Hint: This is equivalent to finding the minimum of
$$\frac{n(7n^2+3)}{34n^2+17}=\frac{n}{34}\left(7-\frac1{2n^2+1}\right)$$
Which for positive numbers, is clearly increasing. So you need to find only the least $n$ satisfying the cubic. 
Checking for $n$ near $\frac{34}7c$ may quickly solve it, depending on the value of $c$.  
