Limit search to a specific folder in website

There is not “blog” folder in WordPress and the search is not done in folders, it is done in the database. I assume you mean limit the search to standard post types.

You could add post_type argument to the search form to include only the standard post type:

<form method="get" class="searchform" action="<?php echo esc_url(home_url()); ?>/">
    <input type="text"
         value="<?php _e( 'Search', 'solofolio' ); ?>"
         name="s"
         id="s"
         onblur="if (this.value == '') {this.value="Search";}"
         onfocus="if (this.value == 'Search') {this.value="";}" />
    <inptu type="hidden" value="post" name="post_type" />
    <span><button type="submit" class="sidebar-search fa fa-search"></button></span>
</form>

Or better, hook in pre_get_post:

add_action( 'pre_get_post', function( $query ) {

    if( $query->is_main_query() && !is_admin() && $query->is_search ) {

        //You can include more post types here if you want
        $query->set( 'post_type', array( 'post' ) );

    }

});

Or even better, and the best way to exclude post types from search, just set the exclude_from_search argument to true when registering the post type.