Use the quadratic formula to solve 5x^2 - 3x - 2 = 0

Problem: Use the quadratic formula to solve $5x^2 - 3x - 2 = 0$.

Steps

1. Identify coefficients
   $$a = 5, \quad b = -3, \quad c = -2$$
2. Apply the quadratic formula
   $$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(5)(-2)}}{2(5)}$$
3. Simplify the discriminant
   $$x = \frac{3 \pm \sqrt{9 + 40}}{10}$$
4. Simplify the square root
   $$x = \frac{3 \pm \sqrt{49}}{10}$$
5. Evaluate the square root
   $$x = \frac{3 \pm 7}{10}$$
6. Calculate the first solution
   $$x_1 = \frac{3 + 7}{10} = \frac{10}{10} = 1$$
7. Calculate the second solution
   $$x_2 = \frac{3 - 7}{10} = \frac{-4}{10} = -\frac{2}{5}$$