RC discharge in two ways, solving for time constant
Yes, you can definitely use Thevenin here.

In the discharge formulas you correctly calculated the time constant as being \$C\$ times the equivalent parallel of \$R_1\$ and \$R_2\$.

There is a mistake on the voltage equation though. Remember that the capacitor is discharging and that its final voltage should be zero. The correct equation should be \$ V(t)=V_0e^{\frac{-t}{R_{eq}C}}\$ instead. This same correction should carry to the current equations.

Welcome to the community! :^)