The back contains many muscles – the latissimus dorsi (lats) are the biggest and broadest middle-back muscles, and these are accompanied by the trapezius (traps) in the upper back heading towards the neck from below and both sides, and also a range of deeper, smaller muscles.
Here’s a workout I used while in the USA recently. It uses machines exclusively, and the workout for back typically uses a higher percentage of machine-based exercise compared to free weights. Its easy to devise pushing exercises with free weights, less so for pulling exercises – the single arm dumbbell-row is a notable exception.
I doubt you’ll have exactly the same machines in your gym (unless it’s the same one I recorded this of course!). But I am sure there are machines which reproduce the same movement.
Give this a go – once a week is ideal – keep the form good, and see how the numbers improve over time.
See the video here.