Bisection method
Think about a continuous function F(x). If the curve of F(x) passes through the x-axis, it means that there must be one specific x number which makes F(x) = 0, in other words, a solution. But how to judge whether the curve passes the x-axis or not? We pick one section with lower boundary a1 and upper boundary b1. Then we calculate F(a) and F(b). If F(b) has different signal with F(a) (or F(a)*F(b) < 0), the F(x) curve will pass through the x-axis in this section, which means F(x) must have a solution in this section. In this way, we can estimate a range of the solution.