I have a broken blood vessel inside my eye. the optomologist used a laser for repair. how long will it take to improve my blurred vision?

Depends: The blur is probably due to blood in the vitreous which can take weeks or months to be absorbed.

Could be a while: Often the laser seals the defect but blood and edema fluid must be resorted before the vision recovers. This can take a while! and recovery depends largely on how much damage was done by the alteration in blood supply in the first place!