If you want a proper fix, and don't have a soldering iron or the courage to try, the cheapest way is to find a local electronics repair shop and ask them to resolder it for you. They should have a minimum charge, but for such a small job - it should be possible to simply have it done on the spot and get you going.
To repair this, with a soldering iron, you could attempt to gently reheat the solder just enough to melt the positive red speaker wire back into the existing solder.
Or to redo the job, with some some solder wick, you would heat the existing solder for the red (+) wire with the wick placed in between until it melts and gets soaked by the wick. Ensure the connection surface is clean, or gently wipe with some flux to prepare to solder the red wire, and simply resolder it.
Not having the actual tools for a small job is likely to be cheaper at a repair shop, given that the person is honest and does not charge a whole lot for a few minutes of work, again I would expect a minimum 1hour charge but no more.