In the continuous application and development of network technology, the reform in Internet information will inevitably bring about major changes in college education and teaching. Based on this background, the paper puts forward the influence of ‘Internet+’ on art design education. At the same time, the article explores the influence factors of the Internet on art design teaching based on the non-linear equation model. We use the parameterised cubic clipping algorithm to find the roots of non-polynomial equations. Through performance analysis and comparison, it is found that the root-finding algorithm proposed by us has better parallelism and lower-storage requirements. This algorithm has certain advantages in solving the weight of the factors that influence the Internet to art design teaching.