Connecting PHP with node.js/javascript

"I'm taking data that I need to take into this algorithm from MySQL, and JavaScript just can't do this".

An AJAX request from the JavaScript in your browser to a PHP script on your server is the straightforward solution to this.

To summarise the process: In the request, the JavaScript code sends some relevant parameters about what it wants, PHP receives that data, queries the database, and returns the results in the response to the AJAX request. JavaScript receives this response, reads the data and continues its processing.

Node.js is just another server-side scripting framework, analagous to PHP. Don't let the fact it uses JavaScript as its programming language confuse you. There is absolutely no need to use Node in this scenario, if your existing server-side solution is written in PHP.

Browser-based JS and PHP can communicate with each other very happily using normal HTTP requests (likely initiated via AJAX, so you avoid page refreshes etc). That's the beauty of the web. The client and server can use totally different programming languages and different operating systems, and it makes no difference at all because they simply exchange data using a common protocol (HTTP) which both can understand.

In your php file, inject your results, something like this.

<?php
// function that handle form data and returns results from mysql
// let's call it my_data_function
$results = my_data_function();
?>


<script type="text/javascript">
  var mysql_data = <?php echo json_enode($results)?>
  my_js_function(mysql_data)
</script>

This is the old school way, then there was ajax, now we are talking REST API.
Hope this helps.
Let me know if you need more help.