ABSTRACT
There are many, many different types of equations used in every branch of engineering and science. There are straightforward methods for solving simple, quadratic and simultaneous equations; however, there are many other types of equations than these three. Many equations can only be solved graphically or by methods of successive approximation to the roots, called iterative methods. Three methods of successive approximations are by using the Newton-Raphson formula, the bisection methods, and an algebraic methods. The advantages of Newton's method over other methods of successive approximations is that it can be used for any type of mathematical equation (i.e. ones containing trigonometric, exponential, logarithmic, hyperbolic and algebraic functions), and it is usually easier to apply than other methods. Each successive approximation method relies on a reasonably good first estimate of the value of a root being made.
