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

Starting with the given equation:

x - 3√x = 4

First, let's move the constant term to the other side of the equation:

x - 4 = 3√x

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

(x - 4)^2 = (3√x)^2

Expanding the left side of the equation:

x^2 - 8x + 16 = 9x

Now, let's move all the terms to one side of the equation:

x^2 - 8x - 9x + 16 = 0

Combining like terms:

x^2 - 17x + 16 = 0

Now, we can factor the quadratic equation:

(x - 1)(x - 16) = 0

Setting each factor equal to zero:

x - 1 = 0 or x - 16 = 0

Solving for x:

x = 1 or x = 16

Therefore, the solutions to the equation x - 3√x = 4 are x = 1 and x = 16.