You should really use parameters in your queries
ADOQuery1.SQL.Text:='SELECT usu_administrador, pass_administrador ' +
' from administradores where usu_administrador = :paramadminname';
ADOQuery1.ParamByName('paramadminname').Value := Edit1.Text;
Also, the reason why your query didn't work was that the value in Edit1 must be in quotes for it to work in your SQL
ADOQuery1.SQL.Text:='SELECT usu_administrador,pass_administrador from administradores where usu_administrador='+QuotedStr(Edit1.Text);