Use AutoHotkey. You can replace any string of entered characters with any other string of characters (in any application). Simply place the first string (called a Hotstring) between two double-colons and follow that by the second string:
1) Go to https://autohotkey.com/
2) Download the app (it's free)
3) Install the app
4) Right-click in Windows Explorer > New > AutoHotkey script
5) Name the new file
6) Right-click the file > Edit
7) Paste the above three lines into the script*
8) Save your changes
9) Double-click the file to run it (a small green icon will appear in your tray)
Now anywhere you enter one of the hotstrings (followed by a space), it will be replaced by whatever is to the right. And in Word's Equation Editor, doing so — for the first two hotstrings — will produce a long left-right arrow and the quadratic equation, respectively.
I included the third line to demonstrate that, with this method, you can create shortcuts to quickly enter your email address or anything else (full paragraphs, etc). (Note: you can use any characters you want to create a hotstring.)
*For some reason the script does not work with a backslash in the hotstring but any other character (eg an underscore), or no character, does the trick.