The equation $$10(x-1)(x-2)(x-3) = 1$$ has three real solutions $$a<b<c$$ where
$a =$ ,
$b =$ , and
$c =$ .
Enter your answers with at least six correct digits beyond the decimal point.
Hint: Ask what the solutions are if the right hand side is 0 instead of 1, and use Newton's Method.