'promising solution' is correct and usable in written English.
You could use it in a variety of contexts, for example: "Researchers have identified a promising solution to reduce global poverty."
It represents a promising solution.
A promising solution to overcome this challenge is quantum simulation.
Rail lines are the most promising solution to the nation's transportation problem.
Germain argues that landfills represent a realistic, promising solution to waste processing.
The most promising solution to America's health care crisis is mandatory insurance.
Optical interconnects provide a promising solution to this on-chip interconnect bottleneck.
These people need post-treatment support, and mind-body techniques offer a promising solution.
One promising solution is to recycle the waste by-products from seafood processing plants across China.
An Israeli company believes it has a promising solution: radio waves.
Two recently discovered bacterial enzymes that specifically degrade PET represent a promising solution.
A promising solution is the application of automated electronic control systems to tune the laser parameters.
