How to find Y for corresponding X values (Implicit function, Complex number)

Question

Given is the equation: Y^2 = X^3 + 2*X - 3*X*Y
Assuming the plotted sketch is correct.

Y^2 = X^3 + 2*X - 3*X*Y

Hint:

Answer 1

Have you used a math library with support for complex numbers ? MathJs is one. See this SO answer.