1. **State the problem:** Find the solution or roots of the quadratic function $f(x) = x^2 - 3x - 7$. 2. **Formula used:** To find the roots of a quadratic equation $ax^2 + bx + c = 0$, use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-3$, and $c=-7$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-3)^2 - 4 \times 1 \times (-7) = 9 + 28 = 37$$ 4. **Apply the quadratic formula:** $$x = \frac{-(-3) \pm \sqrt{37}}{2 \times 1} = \frac{3 \pm \sqrt{37}}{2}$$ 5. **Final answer:** The solutions are $$x = \frac{3 + \sqrt{37}}{2} \quad \text{and} \quad x = \frac{3 - \sqrt{37}}{2}$$ These are the two roots of the quadratic function $f(x)$.