Solve 2x² - 3x - 2 = 0

Step-by-step solution

1. Identify $a = 2$, $b = -3$, $c = -2$.

2. Compute the discriminant: $\Delta = (-3)^2 - 4(2)(-2) = 9 + 16 = 25$.

3. Apply the quadratic formula: $x = \frac{3 \pm \sqrt{25}}{2 \cdot 2} = \frac{3 \pm 5}{4}$.

4. Two solutions: $x_1 = \frac{3 + 5}{4} = 2$ and $x_2 = \frac{3 - 5}{4} = -\frac{1}{2}$.