Difference between 检索 and 找
As @Stan said, 檢索 is usually used with database(資料庫) or library catalog(圖書目錄).

You must have some reference (a catalog, or a list...etc) to be able to 檢索. It's not only formal but more restricted. Whereas 找 can be used very widely.

For example one would say "在資料庫裡檢索資料", "在圖書目錄裡檢索資料", and "在網路上找資料", "在圖書館裡找資料", ...etc.

So you can search (or find) (找) for information  in any suitable places (or under certain conditions). But you would look up (檢索) for information only in restricted places like database.