1. **State the problem:** Solve the quadratic equation $ax^2 + bx + c = 0$ using the quadratic formula. 2. **Formula:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ This formula finds the roots of any quadratic equation where $a \neq 0$. 3. **Example:** Solve $2x^2 - 4x - 6 = 0$. 4. **Identify coefficients:** Here, $a=2$, $b=-4$, and $c=-6$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$ 6. **Apply the quadratic formula:** $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$ 7. **Find the two roots:** - For $+$ sign: $$x = \frac{4 + 8}{4} = \frac{12}{4} = 3$$ - For $-$ sign: $$x = \frac{4 - 8}{4} = \frac{-4}{4} = -1$$ 8. **Answer:** The solutions to the equation $2x^2 - 4x - 6 = 0$ are $x=3$ and $x=-1$. This method works for any quadratic equation by substituting the values of $a$, $b$, and $c$ into the formula and simplifying step-by-step.