Calculating an internal rate of return IRR using quadratic formula

Background: A firm is considering a training program that would cost $150 immediately but would
increase profits by $120 one year later and by $72 in the year after that.
Problem: Use algebra (only) to find the internal rate of return R on that project, to the nearest
percentage point. A correct answer must show a clear sequence of steps, including algebraic
manipulations, and one of those steps must be a quadratic equation that can be solved to find R. A
full credit answer must show the derivation of that quadratic equation and solve it by factorization
or by using the quadratic formula. (An answer that reports only the correct value of R, without
showing the reasoning that produced it, is worth zero points.)
Hint: It may make the problem easier to find a quadratic equation in the variable X = 1 + R, and
then solve that quadratic equation for X. The solution for X then determines the solution for R