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I'm trying to solve the inequality $18bcd - 4b^3d + b^2c^2 - 4c^3 - 27d^2 > 0$ with ${b,c,d} \in \mathbb{R}$ and $c < 0$. The goal is to obtain an expression for $d$.

My guess would be to use solve_ineq() and perhaps assume() for the additional condition, but I can't figure out how. In case of a symbolic equation I'd use

b,c,d = var('b,c,d')
Delta = (18*b*c*d - 4*b^3*d + b^2*c^2 - 4*c^3 - 27*d^2 == 0)
solve(Delta,d)