Jeg kan tænke på to måder, den ene med GROUP_CONCAT og den anden ved at bruge underforespørgsel.
SELECT user_id, GROUP_CONCAT(installed_version) as all_patterns
FROM your_table
GROUP BY user_id
HAVING all_patterns REGEXP 'Pattern 1'
AND all_patterns REGEXP 'Pattern 2';
--
SELECT * FROM
(
SELECT user_id, installed_version FROM your_table
WHERE installed_version LIKE 'Pattern 1'
) as tmp
WHERE installed_version LIKE 'Pattern 2';