Easy, peasy. However, I would not use roots for that, as it will not allow you to distinguish the various roots as they cross paths. As well, it will force you to do the solves in a loop.
syms x w
x_w = solve(-16*x^3 + (14-2*w)*x^2 - (4/3)*x - (w/9 + 5/27) == 0,x,'maxdegree',3);
ezplot(vpa(x_w(1)),[0,1])
ezplot(vpa(x_w(2)),[0,1])
ezplot(vpa(x_w(3)),[0,1])
I won't actually include the graphs here though.
I would point out that you need to remember to use * when you multiply. That is, 2w is not a valid MATLAB expression.
