homework and exercises - Tension force in a rope bringing down a mass

This is the question:

A rope brings a 50 kg object downward at an acceleration of 0.75. What is the tension force of the rope?

I thought that, since the tension and the weight are both "going" downward, the net force would be Weight + Tension = Mass x -Acceleration. The acceleration is negative because it is going downward. But if I do it that way I get the wrong answer. The answer is only correct if net force is Weight - Tension, and if acceleration is positive, neither of which makes sense to me. Can someone explain this?

It could be a silly arithmetic error that I haven't noticed.

Answer

Because the tension points upwards. Notice that the acceleration you gave is less than $g$, and thus $T$ opposes gravity. Choosing the positive axis up, the correct equation is

$$T-mg=ma$$

with $a<0$ as you stated.