Maxima cannot exactly solve this polynomial with not-rational coefficients: 35x^3+(35*sqrt(3)-9)x^2-(9*sqrt(3)+2)x-2*sqrt(3) the real solutions are: -sqrt(3) , -1/7 , 2/5 the only method is: divide( 35x^3+(35*sqrt(3)-9)x^2-(9*sqrt(3)+2)x-2*sqrt(3),x-2/5) and then solve(%,x) Best regards Luigi Marino