Chapter 9 - Quadratic Functions and Equations - 9-6 The Quadratic Formula and the Discriminant - Practice and Problem-Solving Exercises - Page 587: 20

$$x=1.67813371405558,-3.17813371405558$$

$$ \text{The quadratic formula is given by:}$$ $$ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ $$ \text{Plugging in the given values:}$$ $$a=6, b=9, c=-32$$ $$ x = \frac{-9 \pm \sqrt{9^2-4(6)(-32)}}{2(6)}$$ $$\text{Reducing within the radical gives: } $$ $$ x = \frac{-9 \pm \sqrt{849}}{(2)6}$$ $$ \text {This gives: } $$ $$x=1.67813371405558,-3.17813371405558$$