Then to find a,b, and c solve for what terms multiply to if you expanded the above:
Plugging back in:
Multiplying the above out gives something very close to the original polynomial (excepting rounding error)
Now you can find where those 3 terms equal 0 to find the roots, so it changes finding the roots into a problem about solving a set of simultaneous equations. Though if all you are doing is setting the polynomial to 0, it would be easier to divide out the leading 5 coefficient and simplify the formula...