We developed a hybrid optical pump-x-ray probe facility based on the "Kurchatov's synchrotron radiation source" and terawatt (TW) femtosecond laser. The bright x-ray photon source is based on either synchrotron radiation [up to 6 × 1014 photons/(s mm2 mrad2 0.1% bandwidth)] or laser-plasma generators (up to 108 photons/sr/pulse). The terawatt (TW) femtosecond laser pulse initiated phase transitions and a non-stationary "extreme" state of matter, while the delayed x-ray pulse acts as a probe. The synchronization between synchrotron radiation and laser pulses is achieved at 60.3 MHz using an intelligent field-programmable gate array-based phased locked loop. The timing jitter of the system is less than 30 ps. In laser-plasma sources, the x-ray and laser pulses are automatically synchronized because they are produced by using the same laser source (TW laser system). We have reached an x-ray yield of about 106 photons/sr/pulse with 6-mJ sub-ps laser pulses and using helium as a local gas medium. Under vacuum conditions, the laser energy increase up to 40 mJ leads to the enhancement of the x-ray yield of up to 108 photons/sr/pulse. The developed hybrid facility paves the way for a new class of time-resolved x-ray optical pump-probe experiments in the time interval from femtoseconds to microseconds and the energy spectrum from 3 to 30 keV.