Thank you for the opportunity to help you with your question!
Let UNITs guide you; always USE THEM in your calculation to prevent errors
Firstly, the eqn: I- (aq) + I2 (aq) -----> I3- (aq); K = 710 L/mol
K = [i3-]/([i2][i-])
5.00E-2 mol I2 +1.00 liters 5.00E-1 M KI
[KI]init = 5.00E-1 moles/liter
[I2]init = 5.00E-2 moles/liter
[KI]eq = 5.00E-1 moles/liter - x moles/liter
[I2]eq = 5.00E-2 moles/liter - x moles/liter
[I3-]eq = x moles/liter
K= 710 liters/mole = (x moles/liter) / [5.00E-1 - x moles/liter)(5.00E-2 - x moles/liter)]
SOLVE for x
[I3-]/[I2] = x moles I3- / (5.00E-2 - x moles/liter) I2 = ??
Basic mathematics is a prerequisite to chemistry – I just try to help you with the methodology of solving the problem. Please let me know if you need any clarification. I'm always happy to answer your questions.