Current efforts in observational cosmology are focused on characterizing the mass-energy content of the Universe. We present results from a geometric test based on strong lensing in galaxy clusters. Based on Hubble Space Telescope images and extensive ground-based spectroscopic follow-up of the massive galaxy cluster Abell 1689, we used a parametric model to simultaneously constrain the cluster mass distribution and dark energy equation of state. Combining our cosmological constraints with those from X-ray clusters and the Wilkinson Microwave Anisotropy Probe 5-year data gives {\Omega}m = 0.25 +/- 0.05 and wx = -0.97 +/- 0.07 which are consistent with results from other methods. Inclusion of our method with all other techniques available brings down the current 2{\sigma} contours on the dark energy equation of state parameter wx by about 30%.