/* by levanI */

#searchbox{
  background: #eaf8fc;
  width: 500px;
  height: 30px;
  border-width: 1px;
  border-style: solid;
  border-color: #c4d9df #a4c3ca #83afb7;  
  border-radius: 40px;
  padding: 10px;
}
/* by levanI */
#search{
  padding: 5px 9px;
  width: 380px;
  height: 35px;
  border: 1px solid #a4c3ca;
  background: #f1f1f1;
  border-radius: 35px 35px 35px 35px;
  box-shadow:0px 1px 3px rgba(0,0,0,2) inset;
}
#submit{
  background: #6cbb6b;
  width: 100px;
  height: 35px;
  padding: 1px;
  margin: 0px 0px 0px 5px;
  border: 1px solid #7eba7c;
  cursor:pointer;
  font: bold 14px Arial;
  border-radius: 35px 35px 35px 35px;
}

<form id='searchbox'>
  <input type='text' id='search' required placeholder='Search'>
  <input type='submit' id='submit' value='Search'>
</form>