We consider the algebras, with two generators a and b, generated by the quadratic relations ba = α2 + βab + γb2, where the coefficients α, β, and γ belong to an arbitrary field F of characteristic 0. We find conditions for such an algebra to be expressed as a skew polynomial algebra with generator b over the polynomial ring F [a]. These conditions are equivalent to the existence of the Poincaree-Birkhoff-Witt basis, i. e., basis of the form {am, bn}. Bibliography: 16 titles.