Solve 2x^2 - 4x - 3 = 0

Problem: Solve the quadratic equation $2x^2 - 4x - 3 = 0$.

Steps

1. Identify coefficients
   $$a = 2, \ b = -4, \ c = -3$$
2. Apply the quadratic formula
   $$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-3)}}{2(2)}$$
3. Simplify the discriminant and denominator
   $$x = \frac{4 \pm \sqrt{16 + 24}}{4}$$
4. Simplify the square root
   $$x = \frac{4 \pm \sqrt{40}}{4}$$
5. Reduce the radical
   $$x = \frac{4 \pm 2\sqrt{10}}{4}$$
6. Divide numerator and denominator by 2
   $$x = \frac{2 \pm \sqrt{10}}{2}$$