How is the maximum density in a circumstellar disk determined?
If your $r_{peak}$ is not known a priori then you have two unknowns and only one equation: this cannot be solved. At least not without a second equation or a measured $(\rho,r)$-pair (say the central density $\rho_0 = \rho(r=0)$). 

In any case, this definition of radial density looks like an ad-hoc assumption to me, and not something that came out of a proper hydrodynamic model. So without knowing why you chose this form or the context of your disk model I can't comment on what equation is best suited to determine $r_{peak}$. A well-informed guess seems like the way to go.