Cropped linen trousers pulling threads?

Hello everyone

I had bought a pair of linen trousers because I had shortened them myself as they were much too long for me.

I was a bit lazy, so I just cut it, folded it over, and sewed it with the sewing machine.

Everything worked out great and looks good, but after washing it frayed at the bottom and threads are pulling out of the cut part.
I'm afraid that if I wash the pants a few more times they'll fray so much that the seam will come undone again.

Does anyone have any idea what I could do to prevent this?
I saw that there are hem tapes. Could I iron them onto the seam to prevent further fraying? Would this work and stick without a second layer of fabric?

thanks for any help 🙂