Load lines and Esaki diodes
Generally you only get one stable operating point per load line, but in the case of an Esaki tunnel diode you can get two. Take a look at this page for some diagrams of what a load line with two operating points looks like: http://people.seas.harvard.edu/~jones/es154/lectures/lecture_2/load_line/load_line.html .  Basically, you need a line that intersects the I-V curve in two different places where the I-V curve has positive slope.  

The relation $V_in = I_d R + V_d$ relates the I-V curve with the supply voltage and load resistance.  This is the correct formula; there should be two pairs of $I_d$ and $V_d$ that fall on the I-V curve of the diode and will satisfy this relationship for a given $V_in$ and $R$, so long as the load line intersects the I-V curve in more than one place.