[MasterMatt]

I need to calculate the HC and CN bond lengths in HCN give the rotational constants for (HCN) and for deuterated HCN assuming that the isotopic replacement leaves the bond lengths unchanged. From this my plan was to use the equation of the moment of inertia for a linear rotor to write an expression for the moment of inertia for HCN and DCN. Since we're assuming the bond lengths remained unchained I'm just solving one of the expressions for a bond length and plugging it into the other expression. The problem I'm having is that solving one expression for a bond length gives a quadratic and thus two solutions. The math is messy already and I want to avoid plugging this massive thing into the next inertia of expression twice.

[MasterMatt]

And I think putting this into the next inertia expression will give me an ellipsoidal function.

[MrTeo]

The problem I'm having is that solving one expression for a bond length gives a quadratic and thus two solutions. The math is messy already and I want to avoid plugging this massive thing into the next inertia of expression twice.

Do you want to get a formula as an answer or do you have numbers that you can substitute in the expression?

Moreover I think it should be kind of easy to exclude one of the two solutions checking if they're both positive.