Two lights of the same intensity on opposite sides are just going to cause more problems, with double the number of shadows.
There are two factors that determine the hardness of a light source - its size, and its distance from the subject. The further away it is and the smaller it is, the harder it becomes. The sun is an enormous source, but because it is so far away it is incredibly hard when the sky is clear.
Moving your source closer probably isn't an option and will cause all sorts of other problems, so finding away of making it bigger is your only option if you want the shadows to be less harsh. You can do this cheaply and easily by bouncing your light off white polyboard or foamcore, or by shining it through a large sheet of diffusion - it could be translucent shower curtain, a white bed sheet or specially bought diffusion material. Whatever you are shining light through or bouncing it off effectively becomes the source. Either way, making the source larger will make the shadows substantially less hard.
Of course, you may want the hard light on your subject's face, just not the shadows on the wall. For this we need to look at the angle of the light, and flagging it. If the light was below the subject, pointing upwards, the shadows would fall mostly on the wall and ceiling; if the light was level, the shadow would fall partly on the floor, but mostly on the wall. So, if we want to move the shadow from the wall, we need to place the key light above the subject, pointing downwards. You may then want to add some fill light - perhaps with polyboard or a reflector - to prevent the other side of the subject's face from going completely black (this of course depends on the look you are going for).
Finally, let's look at flagging the light. By blocking some of the material with a "flag" - usually a rectangular metal frame covered in black cloth, but anything that blocks the light is usable - we can darken the top of the wall, so that the subject's shadow is no longer so pronounced against a bright wall. It will still be there of course, but much less noticeable. This approach is also useful when the shadow from a microphone boom keeps coming into shot.
So, to summarise: make shadows less harsh by moving your source closer, or making it larger; minimise shadows by changing the angle of your key light or flagging off the light around the subject.