The design and application of artificial neural networks (ANN) for the analysis of several kinds of algebraic equations, both polynomial and linear, are presented in this research. In addition, the different methods for estimating polynomial and linear equations have been examined. The modeling of polynomial and linear equations comes first. The known and unknown coefficients in each algebraic equation have a specific number that aids in identifying the unknown variables. There are several different kinds of polynomial equations, including cubic, quadratic, linear, and biquadratic equations. The number of equations and the number of variables should be equal when solving linear equations. With the use of artificial neural networks (ANN), performance analyses of various linear and polynomial algebraic equations have been made possible. Back propagation delay has been used in the design of the ANN. To find the optimum fit between the measure and reference curves, performance metrics such as accuracy and mean square error (MSE) have been employed. ANN has been found to yield lower mean square error (MSE) and better accuracy when compared to traditional methods.