The most common delta system at 240 volts in the US is a 4-wire + ground configuration where one of the windings has a center tap which is grounded and thus resembles single phase 240/120 volt service. That allows using
240 volt delta loads as well as single phase loads. The voltage from that grounded center tap to the additional phase that is not in line with the center tapped winding is 208 volts. This configuration can be set up one of 3 ways, both involving a standard 240/120 volt center tap transformer. One uses 2 more 240 volt transformers to complete a delta. Another uses a single 208 volt transformer wired to the primary in a way to get a 90 degree phase shift (this arrangement is called a "Scott T"). The third is just an open delta with 1 additional 240 volt transformer instead of two.
A plus for this configuration is that the 240/120 transformer can be made to be a very large one, with smaller additional transformers for cases where the three phase load is small and the single phase load is large.
A negative for this configuration when closed delta is used is that upon one phase loss in the primary, the secondary can backfeed to the dead primary, usually blowing a transformer primary fuse.
Three 139 volt transformers could be used in a WYE configuration to make
240Y/139 which can run most 240 delta loads. Transformers to do this are made, but are usually custom and hard to find. It's half the voltage of the more common 480Y/277 volt system.