In this study, we have solved Einstein field equations for Bianchi type I universe model in Lyra manifold with quadratic equation of state (EoS) p = alpha rho(t)(2) - rho(t). Where alpha not equal 0 is an important constant. Cosmic pressure, density and displacement vector (beta(2)) are related with a constant. In this study beta(2) is a decreasing function of time and behaves like a cosmological constant. These solutions agree with the studies of lialford, Pradhan and Singh, Aygun et al., Agarwal et al., Yadav and liaque as well as SN la observations.