I am the administrator (and currently the sole user) of Jira Core. I cannot find a way to delete tasks. Please help!
Make sure you have "delete" issue permissions in the "project permissions" for the project which contains the task which you want to delete.
https://confluence.atlassian.com/adminjiraserver073/managing-project-permissions-861253293.html
I STRONGLY advise you don't delete issues. This forum is full of people desperatly looking for a way to restore an issue. You can't. It will come around and bite you eventually. I suggest having a resolution of 'deleted' and having a transition that only the project lead can execute that uses a post fuction to set the resolution to deleted and closes the issue. I also have a 'deleted comment' field as required in the transion to explain why it was deleted.
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