To solve this equation, we first need to isolate the square root term on one side of the equation:

√3 - 4x = 2x

Add 4x to both sides:

√3 = 6x

Next, square both sides of the equation to eliminate the square root:

(√3)^2 = (6x)^2

3 = 36x^2

Now, divide by 36 to solve for x:

x^2 = 3/36
x^2 = 1/12

Take the square root of both sides:

x = ±√(1/12) = ±√(1)/√(12) = ±1/(2√3) = ±√3/6

Therefore, the solutions to the equation are x = ±√3/6.