Oracle 11g Release 2

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CREATE TABLE table_name ( event_date ) AS
SELECT DATE '2020-09-08' + INTERVAL '08:55:05' HOUR TO SECOND FROM DUAL UNION ALL
SELECT DATE '2020-09-08' + INTERVAL '15:36:13' HOUR TO SECOND FROM DUAL
2 rows affected

ALTER SESSION SET NLS_DATE_FORMAT = 'YYYY-MM-DD HH24:MI:SS';
SELECT event_date,
       TRUNC( event_date, 'HH' )
         + ROUND( EXTRACT( MINUTE FROM CAST( event_date AS TIMESTAMP ) ) / 15 )
           * INTERVAL '15' MINUTE
         AS rounded_15_event_date
FROM   table_name


EVENT_DATE
ROUNDED_15_EVENT_DATE


2020-09-08 08:55:05
2020-09-08 09:00:00

2020-09-08 15:36:13
2020-09-08 15:30:00


SELECT event_date,
       TRUNC( event_date, 'HH' )
         + ROUND( ( event_date - TRUNC( event_date, 'HH' ) ) * 24 * 4 )
           * INTERVAL '15' MINUTE
         AS rounded_15_event_date
FROM   table_name


EVENT_DATE
ROUNDED_15_EVENT_DATE


2020-09-08 08:55:05
2020-09-08 09:00:00

2020-09-08 15:36:13
2020-09-08 15:30:00

EVENT_DATE	ROUNDED_15_EVENT_DATE
2020-09-08 08:55:05	2020-09-08 09:00:00
2020-09-08 15:36:13	2020-09-08 15:30:00