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Note that even if I appears in the solutions, the solutons are actually real, we can simplify the right-hand side of each solution, and see that I cancel eachother:

sage: s = solve(f==0, x)
sage: [i.rhs().full_simplify() for i in s]
[-1/9*sqrt(3)*(sqrt(3)*cos(1/3*arctan(3/7*sqrt(13)*sqrt(3))) + sqrt(3) - 3*sin(1/3*arctan(3/7*sqrt(13)*sqrt(3)))),
 -1/9*sqrt(3)*(sqrt(3)*cos(1/3*arctan(3/7*sqrt(13)*sqrt(3))) + sqrt(3) + 3*sin(1/3*arctan(3/7*sqrt(13)*sqrt(3)))),
 2/3*cos(1/3*arctan(3/7*sqrt(13)*sqrt(3))) - 1/3]

Note that 0.1 is interpreted as 1/10 in the symbolic ring, so that the solutions are symbolic and not numerical.