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In this paper we devote to study Qian's problem for$\mathcal{L}_{\infty}$-spaces. Firstly, a positive answer to Qian's problem for$C(K)$-spaces is given by the assumption that $K$ has the C$\check{e}$ch-Stoneproperty. Secondly, we obtain quantitative characterizations of separablyinjective spaces that turn out to give a positive answer to Qian's problem of1995 in the setting of separable universality. Thirdly, we prove a sharpenquantitative and generalized Sobczyk theorem, which gives sharpen constants($\alpha,\gamma$) for Qian's Problem. Finally, we give a more generalizedFigiel theorem for $\mathcal{L}_{\infty}$-spaces.

On Qian's problem for $\mathcal{L}_{\infty}$-spaces