1. **State the problem:** Solve the quadratic equation $$-2x^2 + 6x + 7 = 0$$ using the quadratic formula without simplifying the fraction. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Identify coefficients:** Here, $$a = -2$$, $$b = 6$$, and $$c = 7$$. 4. **Calculate the discriminant:** $$b^2 - 4ac = 6^2 - 4 \times (-2) \times 7 = 36 + 56 = 92$$ 5. **Substitute into the quadratic formula:** $$x = \frac{-6 \pm \sqrt{92}}{2 \times (-2)}$$ 6. **Write the solution in the form requested:** $$x = \frac{-6 \pm 1 \sqrt{92}}{-4}$$ Here, blank 1 = -6, blank 2 = 1, blank 3 = 92, blank 4 = -4. **Final answer:** $$x = \frac{-6 \pm 1\sqrt{92}}{-4}$$