lMix (1 / l1 + 1 / l2 ) = 2   Multiplying both sides by the denominator of the RHS.

lMix / l1 + lMix / l2 = 2   Expanding terms in LHS.

lMix / l1 = 2 - lMix / l2   Subtracting lMix / l2 from both sides.

1 / l1 = 2 - (lMix / l2 ) / lMix   Dividing both sides by lMix.

l1 = lMix / (2 - (lMix / l2 ))   Inverting both sides.

lX = lMix / (2 - (lMix / lRef ))   Substituting X for the unknown wavelength, and Ref for the second wavelength.