Black has material advantage. However, Black’s King is exposed. It is White to move. Is White better, worst or equal? How should White continue? This is a very difficult position to assess. Therefore, take your time and try not to use computer. 
Chess Daily News from Susan Polgar
I think it would go like this, 1.Qa5 check-QA4 blocking check. 2. Qc5 check-QB4 blocking again.3.QxB4 and check mate.
if black were to move it would go 1…Rxh3+ 2.g2xh3 Qe4/d5+ 3.Kh2 Qg2#. so after 1.Qa5+ Kb2 and i dont see what white can do to counter blacks material advantage/mating threat. it seems to me that this is 0-1.
Qa5+ is easily refuted with Kb2 as opposed to Qb4 and seems to gain nothing from this move.
I see no way out of this jam for white barring some serious mistakes from black.
after
1.qa5+ Kb2
black threats mate e.g.
2.rf1 rxh3+
3.gxh qe4+
4.kh2 qg2#
nearly the same story after
2.rg1 rxh3+
3.gxh qxg1#
but what, if the white rook would take the field e4 – preventing 3. … qe4+ (the field d5 is shielded by the white queen on a5!)
thus 2.re1! seems to be a good move!
1.qa5+ kb2
2.re1!
eg 2. … rxg2?
3.qb5+ kc2
4.qb3+ kd2
5.rd1+ ke2
6.qc2+ kf3
7.qxg2+ and white will win
my – very short line – up to now is:
1.qa5+ kb2
2.re1 r7g5
3.re2+ kc1
4.re1+ kc2 =
but I’m sure, more competent lines will come
greetings from Vohaul
If played perfectly, White can draw.
Best wishes,
Susan Polgar
http://www.PolgarChess.com
http://www.SusanPolgar.com