Use the update method of the client to execute the update query object.
See the example code below.
<?php
require(__DIR__.'/init.php');
htmlHeader();
// create a client instance
$client = new Solarium\Client($config);
// get an update query instance
$update = $client->createUpdate();
// add the delete id and a commit command to the update query
$update->addDeleteById(123);
$update->addCommit();
// this executes the query and returns the result
$result = $client->update($update);
echo '<b>Update query executed</b><br/>';
echo 'Query status: ' . $result->getStatus(). '<br/>';
echo 'Query time: ' . $result->getQueryTime();
htmlFooter();