Three steps to a live demo that requires only a modern browser, not installation, nor plugins.
1. Develop a working version of a Mathematica Manipulate in a desktop installation or the Wolfram Cloud.
Here's one, the familiar Black-Scholes formula for option pricing.
2. Do a CloudDeploy to obtain a unique URL. The result is (try it out!):
https://www.wolframcloud.com/objects/e8c928db-11c8-4de7-906c-d224f66fc716
3. Use EmbedCode on the cloud object from step 2 to generate embeddable HTML, and insert it into your web page
The whole process takes only a couple of minutes. Here's the result, a live, interactive demo:
Note: you may have to allow third-party cookies (for wolframcloud.com) for this to work.