Yes, the equation has no real roots.
To solve this equation, we first move the constant terms to the right side and the terms with x to the left side.
3x² - 4√3x = -4
Next, we square both sides of the equation.
(3x² - 4√3x)² = (-4)²
9x⁴ - 24√3x² + 16x = 16
Next, we move the constant terms to the right side of the equation.
9x⁴ - 24√3x² = -16
Next, we factor the left side of the equation.
(3x² - 8√3)(3x² + 8√3) = 0
Finally, we set each factor equal to zero and solve for x.
3x² - 8√3 = 0
3x² + 8√3 = 0
However, these equations have no real solutions, so the original equation has no real roots.
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