I am having a hard time looking for a straight answer to converting my tempo to quarter notes so I can use my metronome. I have an eight-note = 96 and a dotted-quarter = 56. I am so confused and (I don't know if this helps) the eight-note is next to adagio and the dotted-quarter is next to largo. I know what these terms mean but I don't know if they should affect what value i put in the metronome.
The notation ♪ = 96 means that there are 96 eighth notes per minute. Therefore, there are 96/2 = 48 quarter notes per minute.
Similarly, if ♩. = 56, then there are 56 dotted quarters per minute. Thus, there are 56 x 3 = 168 eighth notes, hence 168/2 = 84 quarter notes per minute.
The tempo indications adagio and largo do not affect the metronome marking. Rather, the metronome marking is given as a further specification of the tempo. However, it is not necessary to specify the tempo by a value; the indications adagio and largo are clear enough to determine the composer's intention.
However, if a composer writes the tempo in terms of ♪ or ♩., that is usually because the music is felt in eighth notes or dotted quarters rather than in quarters. Therefore, it could be better (depending on context) to set your metronome to the specified tempo rather than converting it to quarter notes per minute.
More advanced metronomes can also beat subdivisions for time signatures like 6/8 and 12/8 (where a tempo is more likely to be specified in ♩. rather than ♩). This could help you as well.