Here's a breakdown:
* 1846: Urbain Le Verrier and John Couch Adams, independently, predicted the existence of a planet beyond Uranus based on its unusual orbital irregularities.
* September 23, 1846: Johann Gottfried Galle, using Le Verrier's calculations, observed Neptune in the sky.
So, while September 23, 1846, is the date of the first confirmed observation of Neptune, the "finding" was a culmination of several years of calculations and predictions.