1. **State the problem:** Solve the quadratic equation $$x^2 - 7x + 10 = 28$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$x^2 - 7x + 10 - 28 = 0$$ which simplifies to $$x^2 - 7x - 18 = 0$$. 3. **Use the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. Here, $$a=1$$, $$b=-7$$, and $$c=-18$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-7)^2 - 4 \times 1 \times (-18) = 49 + 72 = 121$$. 5. **Find the roots:** $$x = \frac{-(-7) \pm \sqrt{121}}{2 \times 1} = \frac{7 \pm 11}{2}$$. 6. **Calculate each root:** - $$x_1 = \frac{7 + 11}{2} = \frac{18}{2} = 9$$ - $$x_2 = \frac{7 - 11}{2} = \frac{-4}{2} = -2$$ 7. **Final answer:** The solutions are $$\boxed{\{9, -2\}}$$ which corresponds to option B.