My Arduino smokes every time I connect an AC/DC wall adapter to it. Can someone help me to fix it?
As already stated in the comments, the voltage of your power supply is the problem. The Arduino has a linear voltage regulator at the Vin pin. It dissipates the excess voltage as heat. The higher the supplied voltage, the lower the current, that you can draw before it overheats. The regulator on a genuine Arduino should go into thermal shutdown, while the regulators on most cheap clones will just get destroyed.

19.5V is too high for the Arduino. The Vin pin is meant for  6 to 12V max. You need a power supply, that can provide a voltage in that range. Or you can buy a regulated power supply, that directly gives you the 5V, that the Arduino needs.

Also you should be really carefull with powering the motor through the Arduinos 5V pin. Motors can easily draw a big amount of current. When drawing too much current through the Arduino (to be specific: through the voltage regulator or the protection diode), the same as explained above will happen. Only very small motors can be supplied through the Arduino. As you use a relay to control it, I guess the motor draws a lot of current. You need tp connect it directly to a fitting power supply, so that the current for it does not flow through the Arduino.

And always be sure, that the used parts can work with the voltage, that you want to supply, including the motor.