Na szczęście nie mam gorączki, więc mogę iść do pracy.

This is a fixed Polish expression. Literally, na szczęście does look like for luck / upon luck / on happiness, but idiomatically it means fortunately or luckily.

You can think of it as a set phrase that learners should memorize as a whole.

• na szczęście = fortunately / luckily
• opposite: na nieszczęście = unfortunately

It is often placed at the beginning of the sentence, but it can also appear elsewhere:

• Na szczęście nie mam gorączki.
• Nie mam na szczęście gorączki.
  This is possible, but less neutral.

In Polish, to say you have a fever, you use the verb mieć (to have):

• mam gorączkę = I have a fever

So the structure is the same as in English: have + fever.

You would not say jestem gorączką, because that would literally mean I am a fever, which makes no sense.

As for nie mam gorączka: after mam, the noun would normally be in the accusative, but because the verb is negated (nie mam), Polish usually uses the genitive instead. That is why it becomes:

• mam gorączkę = I have a fever
• nie mam gorączki = I do not have a fever

This is a very important Polish grammar point.

The noun gorączka is feminine. Its forms here are:

• gorączka = nominative
• gorączkę = accusative
• gorączki = genitive

With mieć in an affirmative sentence, Polish normally uses the accusative:

• Mam gorączkę. = I have a fever.

But with negation, Polish commonly uses the genitive:

• Nie mam gorączki. = I do not have a fever.

This is a very common pattern:

• Mam czas. = I have time.
• Nie mam czasu. = I do not have time.
• Mam samochód. = I have a car.
• Nie mam samochodu. = I do not have a car.

So gorączki is not random — it is the expected genitive form after nie mam.

Więc means so, therefore, or thus.

In this sentence:

• Na szczęście nie mam gorączki, więc mogę iść do pracy.
• Fortunately I don’t have a fever, so I can go to work.

It connects the first idea to the result:

• no fever -> can go to work

It is very common in everyday speech.

Some similar words are:

• więc = so / therefore
• dlatego = therefore / that’s why
• zatem = therefore / thus (more formal)

In Polish, a comma is normally used before coordinating conjunctions like więc, especially when they connect two clauses.

Here the sentence has two parts:

1. Na szczęście nie mam gorączki
2. więc mogę iść do pracy

Because these are two connected clauses, the comma is standard:

• ..., więc ...

This is similar to English, where you often write:

• I don’t have a fever, so I can go to work.

Mogę is the 1st person singular form of móc (can / be able to).

So:

• mogę = I can
• możesz = you can
• może = he/she/it can
• możemy = we can

In the sentence:

• mogę iść = I can go

This is a very common pattern in Polish:

• mogę pracować = I can work
• mogę jechać = I can go/travel by vehicle
• mogę iść = I can go (on foot / go in the general sense)

Both are related, but they are different aspects:

• iść = imperfective
• pójść = perfective

Very roughly:

• iść focuses on the action of going
• pójść often focuses on a single completed act of setting off / going

After móc, both can appear, but they suggest slightly different things:

• mogę iść do pracy = I can go to work
  Neutral, very natural here.
• mogę pójść do pracy = I can go to work / I can head off to work
  Also possible, often a bit more about a specific trip or decision to go.

In this sentence, mogę iść do pracy sounds very natural and general: I am well enough / allowed / able to go to work.

Do usually takes the genitive case in Polish.

The noun is:

• praca = work

Its genitive singular form is:

• pracy

So:

• do pracy = to work

This is one of the most common movement expressions in Polish:

• idę do domu = I’m going home
• jadę do szkoły = I’m going to school
• wracam do pracy = I’m returning to work

So pracy is genitive because of the preposition do.

Yes. Iść do pracy literally means to go to work, and it is a very normal everyday expression.

Examples:

• Idę do pracy. = I’m going to work.
• Muszę iść do pracy. = I have to go to work.
• Nie chcę iść do pracy. = I don’t want to go to work.

If you are traveling by vehicle, Polish may also use jechać:

• Jadę do pracy. = I’m going to work / driving/riding to work.

So:

• iść often suggests going on foot, but in many everyday contexts it can also be used more generally
• jechać is used when the mode of transport matters

Yes, Polish word order is more flexible than English, though some orders sound more natural than others.

The neutral order here is:

• Na szczęście nie mam gorączki, więc mogę iść do pracy.

You could also hear:

• Nie mam gorączki, więc na szczęście mogę iść do pracy.
• Mogę więc iść do pracy.

But changing word order often changes emphasis, not the basic meaning.

For a learner, the original sentence is a very natural, standard order:

1. discourse marker: Na szczęście
2. main statement: nie mam gorączki
3. consequence: więc mogę iść do pracy

These words are tricky because of Polish consonant clusters and nasal vowels.

A rough pronunciation guide:

• na szczęście ≈ na SHCHEN-shche
• gorączki ≈ go-RONCH-kee
• więc ≈ vyents

A few details:

• sz sounds like English sh
• cz sounds like ch in chop
• szcz is a cluster combining those sounds, approximately shch
• ę is a nasal vowel; before some consonants it may sound more like en/em
• ą is also nasal; before czk it often sounds roughly like on

So learners often pronounce:

• szczęście roughly as SHCHEN-shche
• gorączki roughly as go-RONCH-kee

That is only approximate, but it helps at first.

Yes. Gorączka is the standard everyday word for fever.

Examples:

• Mam gorączkę. = I have a fever.
• Masz gorączkę? = Do you have a fever?
• Wysoka gorączka = high fever

Related health words:

• ból = pain
• kaszel = cough
• katar = runny nose
• przeziębienie = cold
• choroba = illness

Yes. Móc can mean both can / am able to and may / am allowed to, depending on context.

So:

• mogę iść do pracy

can mean:

• I can go to work because I’m physically able
• I can go to work because it’s permitted
• I can go to work because the situation allows it

In this sentence, because it mentions not having a fever, the most natural reading is:

• I’m able to go to work / I’m well enough to go to work

So the health context makes the meaning clear.