The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\frac{ 1 }{ 13 }+\frac{ 2 }{ 39 }i\\[1 em]x_2 &= -\frac{ 1 }{ 13 }-\frac{ 2 }{ 39 }i \end{aligned} $$The solutions of $ -2223x^2-342x-19 = 0 $ are: $ x = -\dfrac{ 1 }{ 13 }+\dfrac{ 2 }{ 39 }i ~ \text{and} ~ x = -\dfrac{ 1 }{ 13 }-\dfrac{ 2 }{ 39 }i$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.