A bracket supporting apparatus includes a side plate, two fixing brackets, a first mounting bracket defining a first through hole, and a second mounting bracket defining a second through hole. Each of the two fixing brackets includes a connection portion defining a fixing hole. Two supporting portions extend from two sides of the connection portion. A mounting portion extends from one side of each of the two supporting portions. The two supporting portions of each of the two fixing brackets are substantially parallel to the first mounting bracket and the second mounting bracket. The mounting portions are fixed to the side plate. A first fastener passes through each of the first through holes, the second through holes, and the fixing holes to fix the first mounting bracket and the second mounting bracket to each of the two fixing brackets.