1. **State the problem:** Solve the quadratic equation $$12x^2 - 48 = 0$$. 2. **Formula and rules:** To solve quadratic equations of the form $$ax^2 + bx + c = 0$$, we can isolate $$x^2$$ and then take the square root of both sides. 3. **Step 1: Isolate the quadratic term.** $$12x^2 - 48 = 0$$ Add 48 to both sides: $$12x^2 = 48$$ 4. **Step 2: Divide both sides by 12 to solve for $$x^2$$.** $$\cancel{12}x^2 = \cancel{12}4$$ $$x^2 = 4$$ 5. **Step 3: Take the square root of both sides.** $$x = \pm \sqrt{4}$$ $$x = \pm 2$$ 6. **Final answer:** The solutions to the equation are $$x = 2$$ and $$x = -2$$.