Evidence:
The United States Geological Survey(USGS) website has a lot of indepth material about how the age of the Solar System was determined. The basics of it are that all material radioactively decays into a stable isotope. Some elements decay within nanoseconds while others have projected half-lives of over 100 billion years. The USGS based their study on minerals that naturally occur in rocks and have half-lives of 700 million to 100 billion years. These dating techniques, known as radiometric dating, are firmly grounded in physics and are used to measure the last time that the rock being dated was either melted or disturbed sufficiently to re-homogenize its radioactive elements. These techniques returned an approximate age for meteorites of 4.6 billion years and Earth bound rocks around 4.3 billion years.
http://www.universetoday.com/15575/how-old-is-the-solar-system/
Oh, you want to talk about radiometric dating now?