Find the root of the equation 2x\(^2\) - 3x - 2 = 0

To find the root(s) of the quadratic equation 2x\(^2\) - 3x - 2 = 0, we can use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ where a, b, and c are the coefficients of the quadratic equation ax\(^2\) + bx + c = 0. In this case, a = 2, b = -3, and c = -2. Substituting these values into the formula, we get: $$x = \frac{-(-3) \pm \sqrt{(-3)^2-4(2)(-2)}}{2(2)}$$ Simplifying: $$x = \frac{3 \pm \sqrt{9+16}}{4}$$ $$x = \frac{3 \pm \sqrt{25}}{4}$$ We can simplify the square root to get: $$x = \frac{3 \pm 5}{4}$$ So the roots are: $$x = \frac{3 + 5}{4} = 2$$ $$x = \frac{3 - 5}{4} = -\frac{1}{2}$$ Therefore, the answer is x = -1/2 or 2.