Need super quiet exhaust fan

The quietest solution is to put the fan on the roof (one storey) or on an exterior side wall (if there are floors above you) and connect a duct to the equipment room ceiling.

Regardless how you decide to do it, you also need to think about where the makeup air is coming from. If it's coming under the equipment room door (undercut) it could have a lot of dust in it. Better to install a "transfer grill" and filter, in the door or interior partition wall of the equipment room.

Nsgarch's solution is clearly a better mousetrap. Outside of that, Wpines is right. Panasonic is the way to go. For a ceiling mounted fan, they are spooky quiet.

Thanks guys. I like Nsgarch solution.

Again, Nsgarch is correct.
Don't use a metal duct hose to avoid more vibration.
Try www.build.com to find silent fans

If you don't want to hear it, the fan *must* be remote from the room, with generously sized lined ductwork between the room and the fan, with at least one elbow. Use an aluminum or cast grille, not a cheap stamped steel one, at the room, and no damper (dampers generate noise). For 150 CFM I'd use at least a 12x8 duct...the lower the air velocity the less the noise.

For makeup air the transfer grilles, optionally with a filter between, are a reasonable choice. If the space from which the makeup air is coming is noisy, you will want lined ductwork with one or two elbows in it between the transfer grilles. A door undercut would have to be too large to transfer 150 CFM.