1. We start with the first equation: $3x^{2} - 4 = 1(-x - 2)$. 2. Distribute the right side: $3x^{2} - 4 = -x - 2$. 3. Move all terms to one side to set the equation to zero: $$3x^{2} - 4 + x + 2 = 0$$ which simplifies to $$3x^{2} + x - 2 = 0$$. 4. This is a quadratic equation in standard form $ax^{2} + bx + c = 0$ with $a=3$, $b=1$, and $c=-2$. 5. Use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$ 6. Calculate the discriminant: $$b^{2} - 4ac = 1^{2} - 4 \times 3 \times (-2) = 1 + 24 = 25$$. 7. Substitute values into the formula: $$x = \frac{-1 \pm \sqrt{25}}{2 \times 3} = \frac{-1 \pm 5}{6}$$. 8. Calculate the two solutions: - For $+$: $$x = \frac{-1 + 5}{6} = \frac{4}{6} = \frac{2}{3}$$ - For $-$: $$x = \frac{-1 - 5}{6} = \frac{-6}{6} = -1$$ 9. Final answer: $$x = \frac{2}{3} \text{ or } x = -1$$.