1. **State the problem:** Solve the quadratic equation $3x^2 - 48 = 0$ for $x$. 2. **Rewrite the equation:** $$3x^2 - 48 = 0$$ 3. **Isolate the $x^2$ term:** $$3x^2 = 48$$ 4. **Divide both sides by 3:** $$\cancel{3}x^2 = \cancel{3}16$$ $$x^2 = 16$$ 5. **Take the square root of both sides:** $$x = \pm \sqrt{16}$$ 6. **Simplify the square root:** $$x = \pm 4$$ **Final answer:** $$x = 4 \text{ or } x = -4$$