JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.0/jquery.min.js"></script>
<script src="//maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="//maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css">
<section id="main-slider" class="no-margin">
    <div class="carousel slide">
        <ol class="carousel-indicators">
            <li data-target="#main-slider" data-slide-to="0" class="active"></li>
            <li data-target="#main-slider" data-slide-to="1"></li>
            <li data-target="#main-slider" data-slide-to="2"></li>
            <li data-target="#main-slider" data-slide-to="3"></li>
        </ol>
        <div class="carousel-inner">

            <div class="item active" style="background-image: url(http://www.builtbyevolve.com/images/plugins/nerve-slider/splash.jpg)">
                <div class="container">
                    <div class="row slide-margin">
                        <div class="col-sm-6">
                            <div class="carousel-content">


                            </div>
                        </div>

                        <div class="col-sm-6 hidden-xs animation animated-item-4">
                        </div>

                    </div>
                </div>
            </div><!--/.item-->
            <div class="item" style="background-image: url(http://www.jssor.com/demos/img/home/02.jpg)">
                <div class="container">
                    <div class="row slide-margin">
                        <div class="col-sm-6">
                            <div class="carousel-content">
                                <h1 style="color: deeppink;" class="animation animated-item-1">Servis pro ženy</h1>
                                <h2 class="animation animated-item-2">Vyslechneme Vás!</h2>
                                <a class="btn-slide animation animated-item-3" style="background-color: deeppink;" href="../zeny.php">Číst více!</a>
                   ...

CSS

#main-slider {
  position: relative;
}

.no-margin {
  margin: 0;
  padding: 0;
}

#main-slider .carousel .carousel-content {
  margin-top: 0px;
}

#main-slider .carousel .slide-margin{
  margin-top: 0px;
}

#main-slider .carousel h2 {
  color: #fff;
}

#main-slider .carousel .btn-slide {
  padding: 8px 20px;
  background: #c52d2f;
  color: #fff;
  border-radius: 4px;
  margin-top: 25px;
  display: inline-block;
}

#main-slider .carousel .slider-img{
  text-align: right;
  position: absolute;
}


#main-slider .carousel .item {
  background-position: 50%;
  background-repeat: no-repeat;
  background-size: cover;
  left: 0 !important;
  opacity: 0;
  top: 0;
  position: absolute;
  width: 100%;
  display: block !important;
  height: 300px;
  -webkit-transition: opacity ease-in-out 500ms;
  -moz-transition: opacity ease-in-out 500ms;
  -o-transition: opacity ease-in-out 500ms;
  transition: opacity ease-in-out 500ms;
}

#main-slider .carousel .item:first-child {
  top: auto;
  position: relative;
}

#main-slider .carousel .item.active {
  opacity: 1;
  -webkit-transition: opacity ease-in-out 500ms;
  -moz-transition: opacity ease-in-out 500ms;
  -o-transition: opacity ease-in-out 500ms;
  transition: opacity ease-in-out 500ms;
  z-index: 0;
}

#main-slider .prev,
#main-slider .next {
  position: absolute;
  top: 50%;
  background-color: #c52d2f;
  color: #fff;
  display: inline-block;
  margin-top: -25px;
  height: 40px;
  line-height: 40px;
  width: 40px;
  line-height: 40px;
  text-align: center;
  border-radius: 4px;
  z-index: 0;
}

#main-slider .prev:hover,
#main-slider .next:hover {
  background-color: #000;
}

#main-slider .prev {
  left: 10px;
}

#main-slider .next {
  right: 10px;
}

#main-slider .carousel-indicators li {
  width: 20px;
  height: 20px;
  background-color: #fff;
  margin: 0 15px 0 0;
  position: relative;
}

#main-slider .carousel-indicators li:after {
  position: absolute;
  content: "";
  width: 24px;
  height: 24px;
  border-radius:...

JavaScript

//#main-slider
    $(function() {
        $('#main-slider').carousel({
            interval: 5000,
            cycle: 'true'
        });
    });