SyntaxError: missing ) after argument list

You had a unescaped " in the onclick handler, escape it with \"

$('#contentData').append("<div class="media"><div class="media-body"><h4 class="media-heading">" + v.Name + "</h4><p>" + v.Description + "</p><a class="btn" href="" + type + ""  onclick=\"(canLaunch('" + v.LibraryItemId + " '))\">View &raquo;</a></div></div>")