Chapter 8.2, Problem 47MS

Algebra roulette. Your math instructor has created a special roulette wheel. It has 32 spaces marked with x and four spaces marked with $x^2$. To play the game, you spin the wheel and earn M&Ms. If it stops on a space marked x, the number of M&Ms you win equals x. If it stops on a space marked $x^2$, the number of M&Ms you win equals $x^2$. Your instructor tells you that x satisfies the equation $4x^2+32x=80.$

Determine how many candies you would win for each outcome of a spin of the wheel. What is the probability you will win $x^2\text{M\&Ms?}$