20. \( \sqrt{3 x-6}+4=0 \)

To solve the equation \( \sqrt{3x-6} + 4 = 0 \), we first isolate the square root term: \[ \sqrt{3x-6} = -4 \] However, a square root cannot be negative in the realm of real numbers. This means there are no real solutions to this equation. Now, if you wanted to explore complex solutions, you'd need to square both sides, but remember—you're still dealing with an equation that stems from a square root, so tread carefully! Always check your results by plugging solutions back into the original equation to ensure they satisfy it. In this case, you’ll find that you won't get any valid real numbers. How puzzling, right?