I've given the following equation

$$
f(x) = \text{A}\cdot\sum\_{i=1}^{6}\frac{1}{\text{B}\_i}\Bigl(1-\exp\Bigl(-\frac{x}{\text{C}\_i}\Bigr)\Bigr)
$$

where $\text{A}$, $\text{B}\_i$ and $\text{C}\_i$ are real constants > 0. For a given value of $f(x)$ I now want to determine $x$.

If $i=1$, then there's a simple analytical solution possible.

It seems to me that if $i>1$ this is not longer the case and the equation has to be solved numerically. - Is that true? Or is ist possible to solve this equation analytically for $x$ when $i>1$?

If there doesn't exist an analytical solution which numerical method would you suggest to use in order to Keep the numbers of iterations low?

Thanks for your answers,