I have the following equation: \begin{equation} (y-1)^a - C~~ y~~ \exp(b x)=0 \end{equation}
where $a, b$ are real constants, $C$ may be a complex number. I need to find the real solution of the above equation for each choice of $x$, with $x \in [-100, 100]$. I tried with $\mathbf{fzero, fsolve}$ in matlab. But it does not work. I also tried to solve with Newto - Raphson method. The outcome is negative.
Is it possible to solve it in some other way. Any help/suggestion/advice, will be very useful. Thanks.