public string GetContentType()

public async Task DeletingAttachments()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
        using (Table inspectionTable = geodatabase.OpenDataset<Table>("luCodeInspection"))
        {
            QueryFilter queryFilter = new QueryFilter { WhereClause = "ACTION = '1st Notice'" };

            using (RowCursor cursor = inspectionTable.Search(queryFilter, false))
            {
                while (cursor.MoveNext())
                {
                    using (Row currentRow = cursor.Current)
                    {
                        IReadOnlyList<Attachment> rowAttachments = currentRow.GetAttachments(null, true);
                        IEnumerable<Attachment> attachments = rowAttachments.Where(attachment => attachment.GetContentType().Equals("application/pdf"));

                        IReadOnlyList<long> attachmentIDs = attachments.Select(attachment => attachment.GetAttachmentID()) as IReadOnlyList<long>;
                        IReadOnlyDictionary<long, Exception> failures = currentRow.DeleteAttachments(attachmentIDs);

                        if (failures.Count > 0)
                        {
                            //process errors
                        }
                    }
                }
            }
        }
    });
}