You will want to determine your screen size before you can decide on a projector, and you will need a better projector which offers interchangeable lenses to handle the long throw distance.
This is very normal, and there are a number of projectors on the market which will suit your needs just fine.
But, screen size (16:9 or 16:10 typically) and the throw distance, and you must adjust your budget accordingly for your required installation needs.
This is the search function to use. I put in a 150" screen diagonal with your 51' lens to screen throw distance and a requirement for a bright wide aspect ratio projector....http://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&mfg=&p=500&p=5000&w=&r=&br=3000&br=30000&ll=<g=&t=&db=&dt=&c=&ar=Wide+%2816%3A9-10%29&dvi=&wr=&pjl=&pjw=&pjh=&td=51&is=150&i=d&tr=&oop=1&sort=brt&sz=15
That Panasonic at the top of the list for $3,000 is a great choice. Very bright, and fairly priced. The necessary lens is typically about $1,000 of added cost to make it work.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.