Well it may fit because that card measures 19.8 cm (7.79 inches) but I don't know how is the internal layout of the case, so don't risk it.
Another thing that Power Supply included with the case is not good, and it may not support the HD 7850. Generic PSU doesn't have the PCI-E connector that your Video Card needs (In this case HD 7850 needs 2 x PCI-E Connectors).
So if you want tell us your budget for a case and a Power Supply so we can help