1. **State the problem:** Solve the quadratic equation $3x^2 + 18 = 5x$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$3x^2 - 5x + 18 = 0$$ 3. **Identify coefficients:** Here, $a = 3$, $b = -5$, and $c = 18$. 4. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 3 \times 18 = 25 - 216 = -191$$ 6. **Interpret the discriminant:** Since $\Delta < 0$, there are no real solutions; the solutions are complex. 7. **Find the complex solutions:** $$x = \frac{-(-5) \pm \sqrt{-191}}{2 \times 3} = \frac{5 \pm \sqrt{191}i}{6}$$ **Final answer:** $$x = \frac{5}{6} \pm \frac{\sqrt{191}}{6}i$$