zero-mean RV $$ with finite fourth moment, probability of being positive

Question

For zero-mean RV $X$ with finite fourth moment, prove that $$ P(X>0)\ge \frac{\mathbb{E}(X^2)^2}{4\mathbb{E}(X^4)} $$

I tried Chebyshev with adding $t$ to both sides, but I could not get forth moment.