I bought a replacement board for my wine cooler and the board came with what I think is called "quick connector" on the two spots where my wired were soldered on the original board.

I don't have a soldering iron anymore, so I wanted to know if there's an easy way to connect my wires to these connector spots. I circled in red and black, where my wires are supposed to go..

Thank you in advance!

 

Feed the wire through the hole and twist the wire on to itself to make it secure. You gotta do what you gotta do.

 

Those look like terminals for 1/4" crimp terminals as in the picture. A crimper costs a few bucks.

 

Welcome to AAC.

If you absolutely can't spend any money then @MrChips solution will work, be sure the terminals are clean (clean them with isopropyl alcohol), and insulating them with some electrical tape would be a good idea. Remember, you are depending entirely on the mechanical connection so be sure it is very good. A poor connection will have a high resistance and for high current applications like supplying power that resistance can result in high heat, and eventual damage to the PCB, and failure.

On the other hand, the solution provided by @Jon Chandler is the right way to do it, and the terminals, in a kit with a crimper can be found at any auto parts store, or a place like Walmart or Harbor Freight. The cheap ones are cheap, and for this one off that will be OK. The tool will almost certainly include a wire stripper which will also be helpful.