J.R. S. answered 09/01/19
Ph.D. University Professor with 10+ years Tutoring Experience
There is no equation, but one can generally determine solubility/miscibility or rank in solubility/miscibility by looking at the structure of the compound.
Methanol = CH3OH. Note the -OH group. This not only makes this molecule polar, but also allows for hydrogen bonding with water (H-OH). This will certainly be soluble/miscible in water.
CBr2H2 = dibromomethane. I can't easily draw the structure here, but do look it up. You will see that it is asymmetrical and has a tetrahedral geometry, so it is polar, but does NOT exhibit hydrogen bonding. Also, the polarity is less than that for methanol. So, it will be soluble/miscible in water, but much less so than methanol.