  We present constraints on the equation of state of dark energy, $w$, and the
total matter density, $\Omega_{\mathrm{M}}$, derived from the
double-source-plane strong lens SDSSJ0946+1006, the first cosmological
measurement with a galaxy-scale double-source-plane lens. By modelling the
primary lens with an elliptical power-law mass distribution, and including
perturbative lensing by the first source, we are able to constrain the
cosmological scaling factor in this system to be $\beta^{-1}=1.404 \pm 0.016$,
which implies $\Omega_{\mathrm{M}}= 0.33_{-0.26}^{+0.33}$ for a flat $\Lambda$
cold dark matter ($\Lambda$CDM) cosmology. Combining with a cosmic microwave
background prior from Planck, we find $w$ = $-1.17^{+0.20}_{-0.21}$ assuming a
flat $w$CDM cosmology. This inference shifts the posterior by 1${\sigma}$ and
improves the precision by 30 per cent with respect to Planck alone, and
demonstrates the utility of combining simple, galaxy-scale
multiple-source-plane lenses with other cosmological probes to improve
precision and test for residual systematic biases.
