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In this work we study quantum non-relativistic three-body systems interacting via Coulomb potential. The solution in this undertaking utilizes and expansion of wave functions using products of Laguerre polynomial, followed by variational adjustment of coordinate scaling parameters. The method used in this study was originally developed by C.L. Pekeris and its advantage stems from recursion relations available for Laguerre polynomial. We developed an implementation of modular C++ code for solving the three-body problem numerically with high precision, improving upon previous works. The stability of three-body systems as well as excitation energies of excited states and ionization energy in the parameter space of charges and masses is investigated.