SQL> set term on echo on time on
20:27:00 SQL> select count(*) from TBLREPORTDELTA;

  COUNT(*)
----------
  38831902

20:29:15 SQL> SET AUTOTRACE TRACEONLY EXPLAIN STATISTICS
20:29:21 SQL> delete from TBLREPORTDELTA;
commit;

38831902 rows deleted.


Execution Plan
----------------------------------------------------------
Plan hash value: 3127137464

-----------------------------------------------------------------------------
| Id  | Operation          | Name           | Rows  | Cost (%CPU)| Time     |
-----------------------------------------------------------------------------
|   0 | DELETE STATEMENT   |                |     1 | 53871   (1)| 00:10:47 |
|   1 |  DELETE            | TBLREPORTDELTA |       |            |          |
|   2 |   TABLE ACCESS FULL| TBLREPORTDELTA |     1 | 53871   (1)| 00:10:47 |
-----------------------------------------------------------------------------

Note
-----
   - dynamic sampling used for this statement


Statistics
----------------------------------------------------------
       2310  recursive calls
   41388971  db block gets
     245981  consistent gets
     244808  physical reads
        839  bytes sent via SQL*Net to client
        722  bytes received via SQL*Net from client
          4  SQL*Net roundtrips to/from client
          2  sorts (memory)
          0  sorts (disk)
   38831902  rows processed

20:48:43 SQL> 
Commit complete.

20:48:43 SQL> 

1) trigger on the table
2) unindexed foreign key from child table(s)

1) check these
2) show us how you checked these
3) tell us what the results of this check mean to you

select distinct table_name, constraint_name
from user_constraints
where constraint_name in (select constraint_name
                          from user_cons_columns
                          where exists (select column_name
                                        from user_cons_columns
                                        minus
                                        select column_name
                                        from user_ind_columns
                                      )
                        )
and constraint_type = 'R'

alternatively...

select table_name,  constraint_name, column_name
from user_cons_columns
where (table_name, column_name) not in (select table_name, column_name from user_ind_columns)
 and  constraint_name in (select constraint_name from user_constraints where constraint_type = 'R')
order by 1,2,3

select ucc.table_name, ucc.constraint_name, ucc.column_name 
from user_cons_columns ucc,  user_constraints uc
where (ucc.table_name, ucc.column_name) not in (select table_name, column_name from user_ind_columns)
 and   ucc.constraint_name = uc.constraint_name
 and   uc.constraint_type = 'R'
 and   uc.delete_rule = 'CASCADE'
order by 1,2,3