wpdb get results doesn’t work with variable

this is my code:

$search_by_input= $_POST["search_by_input"];
$client_id_by_nick_name = $wpdb->get_results('SELECT user_id FROM '. $user_meta_table .' WHERE meta_value=".$search_by_input, ARRAY_A);

it doesn”t work. but when I write the value instead of variable it works:

$client_id_by_nick_name = $wpdb->get_results('SELECT user_id FROM '. $user_meta_table .' WHERE meta_value ="admin"', ARRAY_A);

when I use var_dump for $search_by_input it shows this:

string 'admin' (length=5)

The only difference between that two lines is double quotation(before and after admin in second code.).

So Please tell me how can I fix this problem.
Thanks

Try it:

$search_by_input= $_POST["search_by_input"];
$client_id_by_nick_name = $wpdb->get_results( sprintf( "SELECT user_id FROM `%s` WHERE meta_value="%s";", $user_meta_table, $search_by_input ), ARRAY_A);