Why don't you read the verses which I quoted in their context? If you would have done that then you would see the answer right before your eyes:
"And brought them out, and said, Sirs, what must I do to be saved? 31. And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house. And they spake unto him the word of the Lord, and to all that were in his house" (Acts16:30-32).
When the jailer believe the word of the Lord then he received eternal life:
"That whosoever believeth in him should not perish, but have eternal life" (Jn.3:15).