Rearrange and solve for $N: 16 = \frac{1}{n}\cdot 25 + \frac{n-1}{n} \cdot 218.75$

Question

I need to solve for $N$ to get $16$ with the following formula, I'm very bad a re-arranging though, so does anyone have an answer to this?

$$16 = \frac 1 n \cdot 25 + \frac{n-1} n \cdot218.75$$

Would be great if you can help!

Remark

The question is about portfolio theory and the formula is as follow:

Portfolio variance $= \frac 1n \times $ asset standard deviation $+ \frac{n-1}{n}\times $ asset covariance.

In my case,

Asset standard deviation $= 25$,

Asset covariance $= 218.75$

So for example with $N=2$, portfolio variance $= 20.53$; with $N=20$, portfolio variance $= 15.46$

Could you tell me how to rearrange this now?

Answer 1

Multiplying through by $n$ gives $$ 16n=25+218.75n-218.75 \\ \Rightarrow 193.75=202.75n \\ \Rightarrow n=\frac{193.75}{202.75}. $$