$ perl -le'
sub is_balanced {
   my $string = shift;

   eval("qw($string)");
   return 0 if @$;
   return 1;
}
my $balanced   = "(1 + 2 * (3 + (5/4) + 8) + 6)";
my $unbalanced1 = "(((1 + 2 * (3 + (5/4) + 8) + 6))";
my $unbalanced2 = "(((1 + 2 * (3 + (5/4) + 8) + 6))))";

printf("Is $balanced balanced? %s\n", is_balanced($balanced) ? "yes" : "no");
printf("Is $unbalanced1 balanced? %s\n", is_balanced($unbalanced1) ? "yes" : "no");
printf("Is $unbalanced2 balanced? %s\n", is_balanced($unbalanced2) ? "yes" : "no");
'
Is (1 + 2 * (3 + (5/4) + 8) + 6) balanced? yes
Is (((1 + 2 * (3 + (5/4) + 8) + 6)) balanced? yes
Is (((1 + 2 * (3 + (5/4) + 8) + 6)))) balanced? yes