How do I root my Dell Venue 3830 tablet?
I rooted my 3730 using MyKitBatch from social-design-concepts on XDADevs. It is just a root, not a ROM so it is model agnostic. It hasn't been updated in a year but it works with the 3730 and 3830.

If it doesn't work the OP/dev of mykit created this which they also claim has 3830 support, I have never tested it.