You can proceed as follows, using the dimensions I added to your figure:

1. The x, y coordinates of the tip of the crank are (R sin alpha, R cos alpha)

2. Dimension h is R-y

3. Dimension d is sqrt(R^2-h^2)

4. Finally, dimension D is L+x-d, or:

Now the problem is how to make the angle alpha the independent variable - it's a mess, but after some manipulation I get the folowing quadratic equation:

where c and k are:

This will yield two values for alpha. Take the arcsin to find the corresponding angles, but as always with arcsins be careful to understand which quadrant alpha belongs in.