How do I find an equity partner for my running start-up business?

Try builditwith.me or startuply, these sites are geared towards finding people to help with developing a startup.

As you already have paying clients you are in a good position to approach a local Angel Investor / Venture Capitalist group and sell a portion of your company in exchange for the funding required to hire the talent you need to have your product reach its full potential.

The other option, (more along the lines of what you're saying,) would be to trade a piece of the business directly to someone to finish the project for you. A great way to find these sorts of people would be to attend Developer / IT / Web conferences and events in your area to try and head hunt someone.

I'm actually a co-founder of a web development company that focuses on doing Joint Venture work with individuals similar to yourself. If you're still searching for someone to help you out feel free to send me the details and I'll check into allocating a team for you to take your project to the next level.

Cheers,

I would do a combination of searching those sites above and approaching investors to see who will accept a lower amount of equity, all else (meaning the talent you acquire as a result) being equal.

Don't forget YCombinator is another option for you: http://ycombinator.com/apply.html

Another unique way to approach this is to see if a designer (student, faculty, or recent alumnus) at Stanford University is willing to collaborate with you on your project. If it is compelling enough as a business model you may be able to win funding through BASES (bases.stanford.edu). Let me know if you have any questions about BASES.