How was this equation for finding current written?
Yes, they have been disconnected but in the instant after the switch is opened (t = 0+), the branch containing the capacitor still maintains its voltage (due to stored capacitor charge) and so the voltage across the 25-ohm resistor remains the same and the current through it \$i_x\$ also remains the same, so that it seems, from the perspective of the right half of the circuit, that nothing has changed; the switch isn't open yet! 

So \$i_x(0+)\$ can be calculated using the circuit's state as it was before the switch was opened. Of course, after a while, that current will drop to nothing as the capacitor completely discharges.