Find the roots of the polynomial? (Cardano's Method) $y^3-\frac7{12}y-\frac7{216}$
This is part of Cardano's method, so I've gotten my first root to be:
$y_1=\sqrt[3]{\frac7{432}+i\sqrt{\frac{49}{6912}}}+\sqrt[3]{\frac7{432}-i\sqrt{\frac{49}{6912}}}$
I am at a loss on how to evaluate this. I know this is one of three real roots, but I don't know what to do now.

Doing what G. Sassatelli suggested in her/his answer (all credit being for her/him) and being a little patient, you could arrive to three real roots (this is proven using Cardano) which are $$y_1=\frac{1}{3} \sqrt{7} \cos \left(\frac{1}{3} \tan ^{-1}\left(3 \sqrt{3}\right)\right)$$ $$y_2=-\frac{1}{2} \sqrt{\frac{7}{3}} \sin \left(\frac{1}{3} \tan ^{-1}\left(3
   \sqrt{3}\right)\right)-\frac{1}{6} \sqrt{7} \cos \left(\frac{1}{3} \tan
   ^{-1}\left(3 \sqrt{3}\right)\right)$$ $$y_3=\frac{1}{2} \sqrt{\frac{7}{3}} \sin \left(\frac{1}{3} \tan ^{-1}\left(3
   \sqrt{3}\right)\right)-\frac{1}{6} \sqrt{7} \cos \left(\frac{1}{3} \tan
   ^{-1}\left(3 \sqrt{3}\right)\right)$$
