PHP does not write out hungarian characters from MySQL database

Question

So, I made a searching system test (This code searches items out of the "diakok" named database) and there is a problem with it. When I type in my name (Géró Kristóf) it says there are no names in the database like this, but when I write it as Gero Kristof, it finds that right (but it doesn't write out the name, because of these special letters), while there are é and ó instead of e and o in the database. I tried changing the encoding types also in the database and the code, but nothing works right. (With names which don't have special characters, it works just fine)

<?php
  $keresesi_tipus = 'felhasznalonev';
  $keresesi_kifejezes = trim($_POST['keresesi_kifejezes']);
header("Content-type: text/html; charset=utf-8");
  if (!$keresesi_kifejezes) {
    echo "Nem adott meg keresni való nevet. (1-es hibakód)";
    exit;
  }

  if (!get_magic_quotes_gpc()) {
    $keresesi_tipus = addslashes($keresesi_tipus);
  }
  @ $adatbazis = new mysqli('localhost', 'root', '', 'diakok');
  if (mysqli_connect_errno()) {
    echo "Hiba! Nem sikerült csatlakozni az adatbázishoz. (2-es hibakód)";
    exit;
  }

  $lekerdezes = "SELECT * FROM diakok WHERE ".$keresesi_tipus
                ." LIKE '%".$keresesi_kifejezes."%'";
  $talalat = $adatbazis->query($lekerdezes);
  $talalatok_szama = $talalat->num_rows;

  echo "<p>A keresésnek megfelelő diákok száma: ".$talalatok_szama."</p>";

  for ($i = 0; $i < $talalatok_szama; $i++) {
    $sor = $talalat->fetch_assoc();
    echo "<p><strong>".($i+1).". Teljes neve: ";
    echo htmlspecialchars(stripslashes($sor['teljes_nev']));
    echo "</strong><br /> Felhasználóneve: ";
    echo stripslashes($sor['felhasznalonev']);
    echo "<br /> Kategóriája: ";
    echo stripslashes($sor['kategoria']);
    echo "<br />";
    echo "</p>";
  }
  $talalat->free();
  $adatbazis->close();
?>

Here is a pic about the database: