Anyone should be able to obtain a patent for an invention they made that is novel and non-obvious (indeed, sometimes patents slip through that aren't novel or are obvious). Your patent disclosure's power to prevent others from obtaining valid patents is proportional to how much it renders obvious. It would likely not render obvious all possible equipment for detecting X, thus allowing others to patent equipment for detecting X that is not based on the technologies described in your patent disclosure.
Note that a limitation specifying an intended use (to detect X) is generally not a proper way to limit a claim to a machine (as opposed to a method). In this example, your claim fails to contain any reasonably limiting structural features. Among other possible ways to dispose of the claim, it could be rejected by any example of an "equipment" found in the prior art.
Patent claims that purport to claim all possible machines or methods for achieving an end invariably turn out to be invalid for one reason or another.