根子深

gēnzishēn ㄍㄣ ˙ㄗ ㄕㄣ

    • to have powerful, well-established backing
    • to be deeply rooted among the people

Character by character

Saying俗语俗語

Idiom惯用语 · Rarely used now

Literally
the root is deep
Meaning
Says that someone has powerful, well-established backing. It can also mean being deeply rooted among the common people, which is approving.

Sources