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You could use SymPy's solver instead of Maxima, which is used by default in Sage:

sage: var('a b c')
sage: eq = (a==b-sqrt(b^2-c^2/4))
sage: solve(eq,b, algorithm='sympy')

ConditionSet(b, Eq(a - b + sqrt(4*b**2 - c**2)/2, 0), {(4*a**2 + c**2)/(8*a)})