Have a B&S engine model 285777 on my riding lawnmower. For some reason about 2 weeks ago the engine runs wide open when started. I cannot slow it down. Have checked throttle linkage its OK. What could be causing this. Thanks for help...

Check governor linkage.

Hi,
Governor linkages rarely go out of adjustment. Two possibilities come to mind; broken governor or broken thottle shaft(inside the carb.) The governor limits the RPMs by closing the throttle at a certain speed. The throttle shaft is what the governor hooks to and has the butterfly valve(throttle disc) that shuts the throttle attached to it.
Adjusting the governor is farily straight forward with your engine. The lever is on the left rear of the engine block clamped to the governor shaft by a pinch bolt with a 3/8" nut. Place throttle in full speed position, loosen nut on lever so that it can pivot on shaft, turn shaft fully clockwise, tighten nut and test.
Next is a link to the parts breakdown at:
http://www.mymowerparts.com/pdf/Briggs-&-Stratton-Engine-Parts-Manuals-Parts-List/285700-285799%20ms2792%5b1%5d.pdf
And item #131 on page 4 is the throttle shaft; part #494379. Most any dealer will order it for you with prepayment, none will have it in stock except possible on a used carb.
Peace,
Clarke