Yes, it's possible to solo-mine using your PC. The odds are astronomically small, however. You can look up what hash rate your CPU will get here. The best possible CPU the Xeon Phi 5500 gets 140 MH/s. Current network hash rate is 570,000,000,000 MH/s. So every block, you have a 0.000000000245% chance of finding the block. You'll find one block every 76,000 years if the hash rate were to stay constant.
The electricity costs of running your PC are far, far higher than the expected payoff of mining with your CPU. Heck, the wear and tear on your computer is probably a lot higher cost than that expected payoff.
And note, too that this is the best possible CPU. Your average CPU is about 10x worse.