The IRR Equation is widely used in financial mathematics for different purposes, such as computing the rate of return on investments, calculation of implied volatility, yield to maturity, calculation of interest rates for mortgages and annuities, etc.  However, in general, the IRR equation may have several solutions, which restricts its application.  Thus, the knowledge of how to find these solutions and choose the right one is important.  Our understanding of properites of the IRR equation is not complete.