Chapter 9 - Quadratic Functions and Equations - 9-6 The Quadratic Formula and the Discriminant - Practice and Problem-Solving Exercises - Page 587: 17

$$x=0.156465996625054,-2.55646599662505$$

$$ \text{The quadratic formula is given by:}$$ $$ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ $$ \text{Plugging in the given values:}$$ $$a=5, b=12, c=-2$$ $$ x = \frac{-12 \pm \sqrt{12^2-4(5)(-2)}}{2(5)}$$ $$\text{Reducing within the radical gives: } $$ $$ x = \frac{-12 \pm \sqrt{184}}{(2)5}$$ $$ \text {This gives: } $$ $$x=0.156465996625054,-2.55646599662505$$