How do I delete WhatsApp messages from both sides?

After texting unfortunately a text to a wrong person, the latest version of WhatsApp provides users to delete the send text from both side on a permanent basis but within a time limit of 7 minutes, if you did not delete your wrong texts within 7 minutes after its sending, you will not be able to delete that message from the other way any more( but you can delete it from your device only but not from other devices where the message already should be delivered).

You can delete messages for everyone or just for yourself.

To delete messages for everyone

Deleting messages for everyone allows you to delete specific messages you have sent to either a group or an individual chat. This is particularly useful if you sent a message to the wrong chat or if the message you sent contains a mistake.

Messages you successfully delete for everyone will be replaced with "This message was deleted" in your recipients' chats (*). Similarly, if you see "This message was deleted" in a chat, it means that the sender deleted their message for everyone.

You can only delete messages for everyone for up to seven minutes after sending. Once seven minutes have passed, there is no way to delete messages for everyone. To delete messages for everyone:

1. Open WhatsApp and go to the chat containing the message you wish to delete.
2. Tap and hold the message. Optionally, tap more messages to delete multiple messages at once.
3. Tap Delete at the top of the screen > Delete for everyone.

Note:

• In order for messages to be successfully deleted for everyone, both you and your recipient must be using the latest version of WhatsApp for Android, iPhone or Windows Phone.
• (*) If you or your recipient are not using the latest version of WhatsApp for Android, iPhone or Windows Phone, this feature will not be supported.
• Recipients may see your message before it's deleted or if deletion was not successful.
• You will not be notified if deleting for everyone was not successful.

Source: WhatsApp FAQ - Deleting messages