Existing imaging systems support wide-gamut images like ProPhoto RGB, but most images are typically encoded in a narrower gamut space (e.g., sRGB). To this end, these images can be enhanced by learning to recover the original color values beyond the sRGB gamut, or out-of-gamut values. Current methods incorporate the metadata from the target wide-gamut images to expand the gamut, while preventing distortion of in-gamut values. However, this metadata is hard to obtain in real-world scenarios. In this paper, we propose a novel method that requires no metadata. We formulate gamut expansion as a ``root-finding" problem and learn an equilibrium transformation via a neural network. Specifically, our method defines a dynamic system that keeps in-gamut values stable to prevent color distortion and updates out-of-gamut values recurrently. Therefore, we employ an implicit recurrent mechanism to iteratively extract features, which can effectively mitigate the vanishing gradient problem, and reduce the GPU memory consumption to O(1) complexity. Experiments demonstrate the effectiveness and efficiency of our model, in terms of gamut expansion and color restoration, outperforming state-of-the-art models by 0.40dB, in terms of PSNR, with a size of 40K parameters only.