We derive the transport properties of a quantum impurity system, often realized as a quantum dot, subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz(SBA), a generalization of the traditional Thermodynamic Bethe Ansatz(TBA) to open systems out of equilibrium, we derive some transport results for the small quantum dot, described by Anderson impurity Hamiltonian. Exact dot occupation out of equilibrium and the nonlinear conductance are obtained by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current. The current and dot occupation as a function of voltage are evaluated numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. For the larger quantum dot the Interacting Resonance Level Model is used to describe the strog correlation problem in this system. We show some current vs voltage results and compare with other theoretical results. We conclude with the difficulties we encountered by using this method and suggest some future extensions related to this SBA approach.