Chapter 9 - Quadratic Functions and Equations - 9-6 The Quadratic Formula and the Discriminant - Practice and Problem-Solving Exercises - Page 587: 21

$$x=0.590667290886255,-2.25733395755292$$

$$ \text{The quadratic formula is given by:}$$ $$ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ $$ \text{Plugging in the given values:}$$ $$a=3, b=5, c=-4$$ $$ x = \frac{-5 \pm \sqrt{5^2-4(3)(-4)}}{2(3)}$$ $$\text{Reducing within the radical gives: } $$ $$ x = \frac{-5 \pm \sqrt{73}}{(2)3}$$ $$ \text {This gives: } $$ $$x=0.590667290886255,-2.25733395755292$$