How do I solve the current of this circuit with a diode?
You might consider converting your voltage source and the \$R_1\$ and \$R_2\$ resistor divider pair into an equivalent Thevenin voltage and Thevenin source resistance. Once replaced that way, the remaining circuit is trivial to understand and quite easy to solve. (It also instantly avoids all this, "assume one way, then assume the other way" testing process.)







simulate this circuit &ndash; Schematic created using CircuitLab

All you need to do is work out \$V_\text{TH}\$ and \$R_\text{TH}\$ and decide if \$V_\text{TH}\$ is large enough. I'm sure you can work out the details from there.