In order to give the desired security role the rights to delete computers, you must first create and edit the role, and select to give the privilege of Delete under the Item Tasks section.
The next step is to browse out to Resource\Collections, go to Properties > Security and add the security role with the following rights:
The last step is going into the Resource page and, under the resource folder, go to the defaults folder. Under the defaults folder there is a computer icon and an Organizational Structures folder. Under properties on each of those objects, go to Security and add the Security role with the following rights:
This is based on default configurations and may need to be modified since rights to the source location of the computers is needed in order to give delete rights.