From square of b, take 4ac;
Square root extract, and b subtract;
Divide by 2a; you’ve x, hooray!

I am not sure of the origins of this mnemonic. The earliest version I could find was from J. S. Mackay in 1894, but he says the mnemonic was given to him by a member of the Edinburgh Mathematical Society.

Here’s another mnemonic for the quadratic formula:

The books of philosopher, mathematician, magician, musician, Raymond Smullyan are priceless. If you are not familiar with his work, his autobiography is good place to start.