A compact star model formed by quintessence and ordinary matter is presented, both sources have anisotropic pressures and are described by linear state equations, also the state equation of the tangential pressure for the ordinary matter incorporates the effect of This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.* Corresponding author. 2050144-1 Mod. Phys. Lett. A 2020.35. Downloaded from www.worldscientific.com by 44.224.250.200 on 07/11/20. Re-use and distribution is strictly not permitted, except for Open Access articles. G. Estevez-Delgado et al.the quintessence. It is shown that depending on the compactness of the star u = GM/c 2 R the constant of proportionality µ between the density of the ordinary matter and the radial pressure, Pr = µc 2 (ρ − ρ b ), has an interval of values which is consistent with the possibility that the matter is formed by a mixture of particles like quarks, neutrons and electrons and not only by one type of them. The geometry is described by the Durgapal metric for n = 5 and each one of the pressures and densities is positive, finite and monotonic decreasing, as well as satisfying the condition of causality and of stability v 2 t − v 2 r < 0, which makes our model physically acceptable. The maximum compactness that we have is u ≤ 0.28551, so we can apply our solution considering the observational data of mass and radii M = (2.01 ± 0.04) M ⊙ , R ∈ [12.062, 12.957] km which generate a compactness 0.22448 ≤ u ≤ 0.25448 associated to the star PSR J0348 + 0432. In this case, the interval of µ ∈ [0.78055, 1] and its maximum central density ρc and in the surface ρ b of the star are ρc = 7.0387 × 10 17 kg/m 3 and ρ b = 4.6807 × 10 17 kg/m 3 , respectively, meanwhile the central density of the quintessence ρqc = 3.4792 × 10 16 kg/m 3 .