To solve the equation, we can start by taking the square root of both sides:

√((1/5 - 3/2x)^2) = √(4/9)

Simplifying the right side:

1/5 - 3/2x = ±√(4/9)

Next, let's simplify the square root on the right side:

1/5 - 3/2x = ±(2/3)

Now, we can solve for x by isolating it on one side of the equation:

-3/2x = ±(2/3) - 1/5

To simplify the right side, we need to find a common denominator:

-3/2x = (10/15) - (3/15)

Combining the fractions:

-3/2x = 7/15

To solve for x, we can multiply both sides of the equation by -2/3:

x = (7/15) * (-2/3)

Simplifying:

x = -14/45

Therefore, the solution to the equation is x = -14/45.