For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option

https://andersonjtcn476.zenbloomer.com/posts/ac-services-salt-lake-city-homeowners-commonly-need-over-time-2

For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option, especially where existing heating is radiant, hydronic, or space-heater based.