I dont know about the FirebirdSQL, I have never used it, but I think that you need to enclose the edit1.text in single qutoes, because it is a string. Strings must be quoted with single quotes. And number two, I believe that the equation sign is typed incorectly, it should not be
xxx:='some text'
like in pascal/delphi/lazarus, the SQL correct gramar is just '='
xxx='some text'
SQLQuery1.SQL.Text:='delete from table where xxx=' + #39 + Edit1.Text + #39;
The character #39 is a single quote. This line of code would be same like if you typed to the SQL prompt the following:
delete from table where xxx='this is the text contained in the edit1';