Using recent measurements of angular size of high-z milliarcsecond compact radio sources compiled by Gurvitset al. (1999) and X-ray gas mass fraction of galaxy clusters published by Allen et al. (2002, 2003), we explore their bounds on the equation of state, ωx=px/ρx, of the dark energy, whose existence has been congruously suggested by various cosmological observations. We relax the usual constraint ωx ≥ −1, and find that combining the two databases yields a nontrivial lower bound on ωx. Under the assumption of a flat universe, we obtain a bound −2.22<ωx<−0.62 at 95.4% confidence level. The 95.4% confidence bound goes to −1 ≤ωx<−0.60 when the constraint ωx ≥ −1 is imposed.