Circuit exercise with diodes
You can't solve these kinds of problems with a simple equation because the diodes are non-linear.

You need to consider (analyze) four separate cases: both diodes conducting, neither diode conducting, only D1 conducting, and only D2 conducting. Find the currents through the diodes and the voltages across them in all four cases.

If you assumed that a diode was conducting and you find that a positive current is in fact flowing through it, and if you assumed that a diode was non-conducting and you find that the voltage across it is negative (or less than \$V_f\$), then your assumption is correct. If you analyze a particular case and find that the voltages or currents are inconsistent with the assumptions then you can reject that case.

Once you find the only set of assumptions that is consistent with your analysis, you can go ahead and find \$V_{out}\$.