To solve this equation, we need to first simplify the fractions.

Convert 2 4/5 to an improper fraction:
2 4/5 = (2 * 5 + 4)/5 = 14/5

Now our equation becomes:
1/4x + 5/12 = 14/5 + 7/10

Next, find a common denominator, which in this case is 60:
15/60x + 25/60 = 168/60 + 42/60

Now add the fractions:
15/60x + 25/60 = 210/60

Subtract 25/60 from both sides:
15/60x = 185/60

Divide both sides by 15/60:
x = (185/60) / (15/60)
x = 185/15
x = 37/3

Therefore, the solution to the equation is x = 37/3.