15. Let line $l$ intersect the curve $y=x^{3}+x+1$ at three distinct points $A$, $B$, and $C$, and $|A B|=|B C|=\sqrt{5}$. Then the equation of line $l$ is $\qquad$.
15. $y=2 x+1$.

Notice that, the curve is symmetric about the point $(0,1)$.
Let the equation of the line be $y=k x+1$, and point $A(x, y)$. Then
$$
\left.\begin{array}{l}
\left\{\begin{array}{l}
y=k x+1, \\
y=x^{3}+x+1, \\
\sqrt{x^{2}+(y-1)^{2}}=\sqrt{5}
\end{array}\right. \\
\Rightarrow(k-2)\left(k^{2}+k+3\right)=0
\end{array}\right\}
$$

Therefore, the equation of the required line is $y=2 x+1$.