1. **Problem Statement:** Solve the equation $2x^2 - 8x + 6 = 0$ for $x$. 2. **Formula Used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Identify coefficients:** Here, $a = 2$, $b = -8$, and $c = 6$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-8)^2 - 4 \times 2 \times 6 = 64 - 48 = 16$$ 5. **Evaluate the roots:** $$x = \frac{-(-8) \pm \sqrt{16}}{2 \times 2} = \frac{8 \pm 4}{4}$$ 6. **Find the two solutions:** - For the plus sign: $$x = \frac{8 + 4}{4} = \frac{12}{4} = 3$$ - For the minus sign: $$x = \frac{8 - 4}{4} = \frac{4}{4} = 1$$ 7. **Final answer:** The solutions to the equation are $x = 3$ and $x = 1$.