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First, polynomial rings don't automatically inject their variables in the global name space. You can do this

sage: R = PolynomialRing(RR,['a','b','c','d'])
sage: R.inject_variables()
Defining a, b, c, d

Or use the following short-hand notation to declare the polynomial ring and inject the variables at the same time:

sage: R.<a,b,c,d> = RR[]

Second, you can't mix the symbolic solver with polynomial algebra. To "solve" (what does that even mean since there is no formula for the roots of polynomials of degree > 5) polynomial equations you should rephrase your question in terms of ideals and term orders.