Powerful winds driven by active galactic nuclei are often thought to affect the evolution of both supermassive black holes and their host galaxies, quenching star formation and explaining the close relationship between black holes and galaxies. Recent observations of large-scale molecular outflows in ultraluminous infrared galaxies support this quasar-feedback idea, because they directly trace the gas from which stars form. Theoretical models suggest that these outflows originate as energy-conserving flows driven by fast accretion-disk winds. Proposed connections between large-scale molecular outflows and accretion-disk activity in ultraluminous galaxies were incomplete because no accretion-disk wind had been detected. Conversely, studies of powerful accretion-disk winds have until now focused only on X-ray observations of local Seyfert galaxies and a few higher-redshift quasars. Here we report observations of a powerful accretion-disk wind with a mildly relativistic velocity (a quarter that of light) in the X-ray spectrum of IRAS F11119+3257, a nearby (redshift 0.189) optically classified type 1 ultraluminous infrared galaxy hosting a powerful molecular outflow. The active galactic nucleus is responsible for about 80 per cent of the emission, with a quasar-like luminosity of 1.5 × 10(46) ergs per second. The energetics of these two types of wide-angle outflows is consistent with the energy-conserving mechanism that is the basis of the quasar feedback in active galactic nuclei that lack powerful radio jets (such jets are an alternative way to drive molecular outflows).