Solve the equations exactly in the complex number system. (Find one solution graphically and then use the quadratic formula.) \[ x^{3}=19 x-5 x^{2} \] The solutions are $\square$. (Type an integer or a fraction. Use a comma to separate answers as needed.)

Step 1 ：Solve the equations exactly in the complex number system. (Find one solution graphically and then use the quadratic formula.)

Step 2 ：The equation is \(x^{3}=19 x-5 x^{2}\)

Step 3 ：Rearrange the equation to \(x^{3} - 5x^{2} - 19x = 0\)

Step 4 ：Solve the equation to find the real roots

Step 5 ：The real roots of the equation are \(0\), \(\frac{5}{2} - \frac{\sqrt{101}}{2}\), and \(\frac{5}{2} + \frac{\sqrt{101}}{2}\). These are the solutions to the equation in the complex number system.

Step 6 ：Final Answer: The solutions are \(\boxed{0, \frac{5}{2} - \frac{\sqrt{101}}{2}, \frac{5}{2} + \frac{\sqrt{101}}{2}}\)