Me tranquiliza que la radiografía haya mostrado que no hay fractura.

Literally, me tranquiliza means it calms me or it reassures me.

• tranquiliza = calms / reassures
• me = me

So the structure is:

• Algo me tranquiliza = Something reassures me

In this sentence, the thing that reassures the speaker is the whole following idea:

• que la radiografía haya mostrado que no hay fractura

So the full sense is: It reassures me that the X-ray has shown that there is no fracture.

That que means that.

Spanish often uses que to introduce a whole clause after verbs expressing feelings, reactions, judgments, and similar ideas.

So:

• Me tranquiliza que... = It reassures me that...
• Me alegra que... = I’m glad that...
• Me preocupa que... = It worries me that...

Here, que introduces the thing that is reassuring the speaker.

Because after me tranquiliza que..., Spanish normally uses the subjunctive, not the indicative.

• ha mostrado = present perfect indicative
• haya mostrado = present perfect subjunctive

Since me tranquiliza expresses an emotional reaction, the verb in the following clause is triggered into the subjunctive:

• Me tranquiliza que la radiografía haya mostrado...

This is very common in Spanish:

• Me alegra que hayas venido.
• Me sorprende que lo hayan dicho.
• Me preocupa que no haya llamado.

Because the showing happened before the reassuring reaction.

The sequence is roughly:

1. The X-ray showed something.
2. That result reassures me now.

So Spanish uses the present perfect subjunctive to refer to something completed but still relevant to the present:

• haya mostrado = has shown

Compare:

• Me tranquiliza que la radiografía muestre...
  This would sound more like a general or ongoing idea: It reassures me that the X-ray shows...
• Me tranquiliza que la radiografía haya mostrado...
  This refers to the completed result of the X-ray: It reassures me that the X-ray has shown...

In this sentence, the perfect form fits very naturally.

Because not every clause after que automatically takes the subjunctive.

The first subordinate clause is:

• que la radiografía haya mostrado...

Inside that clause, there is another clause depending on mostrar:

• que no hay fractura

Here, the X-ray result is being presented as a fact or finding: there is no fracture. That is why Spanish uses the indicative:

• mostrar que no hay fractura = to show that there is no fracture

So:

• Me tranquiliza que... triggers the subjunctive in haya mostrado
• But mostrar que... introduces factual content, so hay stays in the indicative

Because haber in expressions like hay is commonly used to state whether something exists or is present.

• hay fractura = there is a fracture
• no hay fractura = there is no fracture

Spanish often omits the article in this kind of existence statement, especially in medical or general descriptive language.

Compare:

• No hay problema.
• No hay señal de infección.
• No hay fractura.

You could sometimes hear no hay una fractura, but that would sound more specific and less natural here.

Here, radiografía means X-ray.

Depending on context, it can refer to:

• the image/result of the X-ray
• the X-ray examination itself

In this sentence, it most naturally refers to the X-ray result/image that revealed the absence of a fracture.

Also note:

• la radiografía is feminine
• plural: las radiografías

In everyday speech, people also say:

• la placa in some contexts
• los rayos X for X-rays as a test or technology

But radiografía is a standard and clear choice.

Yes, in many contexts you could say:

• Me tranquiliza que los rayos X hayan mostrado que no hay fractura.

That is also natural.

The main difference is lexical:

• radiografía often focuses on the X-ray image/result
• rayos X can refer more broadly to the X-ray test or imaging

In practice, both can work, depending on the context and the speaker.

Yes. Spanish allows that word order:

• Que la radiografía haya mostrado que no hay fractura me tranquiliza.

This version puts the whole clause first and is still correct.

The original version:

• Me tranquiliza que la radiografía haya mostrado que no hay fractura.

is often a little smoother and more natural in everyday use, because Spanish commonly places the emotional reaction first and then explains its cause.

All three can work depending on context, but reassures is probably the best fit here.

• calms me = more literal
• reassures me = very natural in this medical context
• relieves me = possible, but slightly less direct as a translation of tranquiliza

So in this sentence:

• Me tranquiliza... = It reassures me...

is usually the most natural English rendering.

Because fractura is the normal medical or semi-medical word for fracture.

In medical contexts, Spanish often prefers the technical noun:

• fractura = fracture

Whereas:

• hueso roto = broken bone

is more informal and descriptive.

Since the sentence refers to what an X-ray showed, fractura sounds very natural and appropriate.

Yes, that is a very natural alternative.

• Me tranquiliza saber que no hay fractura.
  = It reassures me to know that there is no fracture.

This version focuses less on the X-ray itself and more on the fact that the speaker now knows the result.

The original sentence is more specific because it includes the source of the information:

• the X-ray has shown...

So the choice depends on what you want to emphasize.

A useful way to break it down is:

• Me tranquiliza = main clause
• que la radiografía haya mostrado que no hay fractura = noun clause acting as the subject/content of what reassures me

Inside that clause:

• la radiografía = subject
• haya mostrado = verb
• que no hay fractura = clause functioning as the object of mostrar

So the structure is roughly:

• [It reassures me] [that the X-ray has shown] [that there is no fracture].

This is a good example of Spanish stacking clauses with que, which is very common.