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.