Other answers suggest putting a piece of board across the wall, attaching it to the studs, then attaching this hanger to that. There's nothing wrong with that at all, but I thought I'd make another couple of suggestions:
It's hard to tell for sure, but it appears that the "center" hanger for the upper bar is directly above the hanging bar support for the lower bar, and that this support is held up by a board that appears to run all the way to the floor.
If that's the case, replace the short vertical support for this center hanger with a longer one that rests directly on top of the one below it. You can hold it in place by putting a couple of shorter pieces of wood on either side, making a sandwich much like the current hanger, then screwing up from underneath the shelf into these side boards while the center board remains centered directly over the one beneath.
This will transfer the vast majority of the weight of hanging clothes to the board below and then to the floor. The only need for the screws at the bar level will be to keep the bar from tipping away from the wall, not supporting weight. This will put much less stress on these screws and a couple of decent drywall toggles will be more than sufficient to hold them to the wall.
The hanger bars appear to be adjustable width. Find a stud (if this is in the US, there will be one every 16" along that wall, possibly as much as 24" apart, but most likely 16" - similar spacing for most other countries).
Move that center anchor to the stud. Then using the adjustment available in the bars have 2 bars of unequal length, but the same total overall length. This will provide the strength of having the center support attached to something structural. (You may need to be aware of the extra length of one bar and put lighter clothes on that one and the heavier stuff on the shorter bar to
prevent reduce bowing of the longer bar.)
While you're at it (and especially if you move the center support to the right to the nearest stud), confirm that the left-hand support is actually attached to a stud as well. If it's not, now is the time to move it to a stud, instead of waiting for it to rip out of the drywall leaving a big hole to patch instead of a couple of small screw holes.