1. **State the problem:** Solve the quadratic equation $2x^2 + 8x = 960$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$2x^2 + 8x - 960 = 0$$ 3. **Simplify the equation:** Divide every term by 2 to simplify: $$\cancel{2}x^2 + \cancel{2} \cdot 4x - \cancel{2} \cdot 480 = 0 \implies x^2 + 4x - 480 = 0$$ 4. **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, $a=1$, $b=4$, and $c=-480$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 4^2 - 4 \cdot 1 \cdot (-480) = 16 + 1920 = 1936$$ 6. **Find the square root of the discriminant:** $$\sqrt{1936} = 44$$ 7. **Calculate the two solutions:** $$x = \frac{-4 \pm 44}{2}$$ 8. **First solution:** $$x = \frac{-4 + 44}{2} = \frac{40}{2} = 20$$ 9. **Second solution:** $$x = \frac{-4 - 44}{2} = \frac{-48}{2} = -24$$ **Final answer:** The solutions to the equation are $x = 20$ and $x = -24$.