Let u and v be the solutions to 3x^2 + 5x = 7 = 0. Find u^2 + v^2.

By Vieta's Theorem the equation $3x^2+5x=7=0$ gives you the values of $u+v$ and $uv$. Noticing that $u^2+v^2 = (u+v)^2 - 2uv$ should tell you what to do.