  We derive two-sided bounds for moments and tails of random quadratic forms
(random chaoses of order $2$), generated by independent symmetric random
variables such that $\lVert X \rVert_{2p} \leq \alpha \lVert X \rVert_p$ for
any $p\geq 1$ and some $\alpha\geq 1$. Estimates are deterministic and exact up
to some multiplicative constants which depend only on $\alpha$.
