(untitled) (Journal of Information Technologies in Education (ITE), 2018)
All known widespread algorithms of a numerical solution of an equation on a straight line segment assume that segments of isolation of roots are already known. These are such segments, on each of which a solution is one and only one. The method of this work allows to discover all solutions of an equation f(x) = 0 for arbitrary continuously differentiable function f(x) on the set segment of a straight line with the set accuracy. Convergence of the method is exponential. Thus, the method automatically separates roots. In the course of numerical methods it hits in its ideological center, forcing to consider all structure of the theory to make it clear and deepen its understanding. The method of this work is realized in a desktop in language Java.