What you have done is correct. We have to judge the diagram by obtaining the results from the formula but not just simply imagining a diagram. The results suggest that your diagram was wrong and the correct diagram could be the below one: 

[![enter image description here][1]][1]

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Extending the comments:<br/> To get a real image the virtual object should lie in between pole and the focus. We can prove this result from mirror formula. From the sign conventions, we have $f>0$ ,$u>0$ and $v$ should be less than zero (for forming real image).<br/>
So from mirror formula, $ \frac{1}{v}=\frac{1}{f}-\frac{1}{u} <0$ $\implies u<f$

  [1]: https://i.sstatic.net/DMbaXm.jpg