In Porous Media, Displacement Flows Where Two Fluids Are Different In Viscosity Is Much Important For Industry and Biological Applications. Due to Viscosity-Contrast Between the Fluids, Instability Is Developed at the Interface Which Is Known As Viscous Fingering Instability. In This Work, We Discussed About the Equilibrium Solution of the Viscous-Fingering Instability Problem. Advection-Diffusion Equation Is Obtained In Equilibrium State. Hence, Advection-Diffusion Is Discussed In This Paper Which Is Fundamental In Understanding of In- Stability Problem. Our Result Shows That In the Early Time, Solution Is Not Symmetric About the Fluid-Fluid Interface. Our Finding Suggest That Equilibrium State Is Time-Dependent.