how to find equations for current of circuit with transistors?
This is a horrible question, because it's not related to how we'd normally calculate the operating point of this circuit. It's so annoying that rather than try to teach you anything, I'm just going to give you (part of) the answer. I'm doing this because the question isn't well-posed to teach you anything anyway.

You can get \$I_C\$ very simply as 

$$I_C = \frac{V_{DC1}-V_C}{R_C} $$

That's just a simple statement of Ohm's law for RC, in terms of the voltages you were asked to find the current in terms of. So it answers the question as stated.

You can get the current for \$I_B\$ by a very similar statement of Ohm's law for \$R_B\$. I'll let you do that part yourself.

In the real world, of course, this has nothing to do with how you'd find \$I_C\$ in a real circuit, so just give your instructor the answer he wants but don't imagine you're learning much from it.