In plain words
A person of faith, devoted to it and with the senses mastered, attains jñāna; having attained jñāna, one quickly reaches supreme peace.
Word for word
One with faith, intent on it, with senses restrained, gains jñāna; having gained jñāna, he soon reaches the supreme peace.
The commentators
Bhagavadgītābhāṣyam
येन एकान्तेन ज्ञानप्राप्तिः भवति स उपायः उपदिश्यते —
श्रद्धावान् श्रद्धालुः लभते ज्ञानम् । श्रद्धालुत्वेऽपि भवति कश्चित् मन्दप्रस्थानः, अत आह — तत्परः, गुरूपसदनादौ अभियुक्तः ज्ञानलब्ध्युपाये श्रद्धावान् । तत्परः अपि अजितेन्द्रियः स्यात् इत्यतः आह — संयतेन्द्रियः, संयतानि विषयेभ्यो निवर्तितानि यस्य इन्द्रियाणि स संयतेन्द्रियः । य एवंभूतः श्रद्धावान् तत्परः संयतेन्द्रियश्च सः अवश्यं ज्ञानं लभते । प्रणिपातादिस्तु बाह्योऽनैकान्तिकोऽपि भवति, मायावित्वादिसम्भवात् ; न तु तत् श्रद्धावत्त्वादौ इत्येकान्ततः ज्ञानलब्ध्युपायः । किं पुनः ज्ञानलाभात् स्यात् इत्युच्यते — ज्ञानं लब्ध्वा परां मोक्षाख्यां शान्तिम् उपरतिम् अचिरेण क्षिप्रमेव अधिगच्छति । सम्यग्दर्शनात् क्षिप्रमेव मोक्षो भवतीति सर्वशास्त्रन्यायप्रसिद्धः सुनिश्चितः अर्थः ॥ ३९ ॥
In plain words
The means by which knowledge is attained without fail — that is what is taught now —
'One full of faith' obtains knowledge — that's simple enough. But even a faithful person can drag their feet, so the text adds 'devoted to it': diligently pursuing the means of gaining knowledge, like approaching a teacher, while being full of faith. And even someone devoted like that might still have unconquered senses, so it adds once more, 'of controlled senses' — meaning senses withdrawn from their objects and kept in check. Anyone who is faithful, devoted, and self-controlled like this is certain to obtain knowledge. Outward gestures like prostration, being merely external, can be misleading — after all, people can fake sincerity — but that doesn't make faith and the rest the whole exclusive path either. So what comes from gaining knowledge? The text now tells us: 'having gained knowledge, he attains the supreme peace called liberation, that stillness, without delay, swiftly indeed.' That right vision brings liberation swiftly is a truth every scripture's own reasoning firmly establishes — settled beyond doubt.
Close to the Sanskrit
That means by which the attainment of knowledge comes about unfailingly is now taught —
'One full of faith' — the faithful one obtains knowledge. But even a faithful person might be someone slow to actually set out; so he adds — 'devoted to it' — diligently applying himself to approaching a teacher and the rest, the means of gaining knowledge, being full of faith. Even one so devoted might still be one whose senses are unconquered; so he adds again — 'of controlled senses' — one whose senses are controlled, withdrawn from their objects, is one of controlled senses. One who is thus full of faith, devoted, and of controlled senses certainly obtains knowledge. Prostration and other outward acts, however, being external, can be inconclusive too, since hypocrisy and the like are always possible; but that does not mean faith and the rest are the sole, exclusive means to gaining knowledge. And what, further, would follow from gaining knowledge? This is now told — 'having gained knowledge, he attains the supreme peace called liberation, cessation, without delay, quickly indeed' — he attains it. That, from right vision, liberation results quickly indeed — this is a meaning well established by the reasoning of every scripture, thoroughly well-ascertained.