To solve the equation căn(4-5x) = 12, we need to isolate the variable x.

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

(4-5x)^2 = 12^2
16 - 40x + 25x^2 = 144

Rearrange the equation to form a quadratic equation:

25x^2 - 40x + 16 - 144 = 0
25x^2 - 40x - 128 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, factoring is not possible, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Using the quadratic formula, we have:

x = (-(-40) ± √((-40)^2 - 4(25)(-128))) / (2(25))
x = (40 ± √(1600 + 12800)) / 50
x = (40 ± √14400) / 50
x = (40 ± 120) / 50

This gives us two possible solutions:

x1 = (40 + 120) / 50 = 160 / 50 = 3.2
x2 = (40 - 120) / 50 = -80 / 50 = -1.6

Therefore, the solutions to the equation căn(4-5x) = 12 are x = 3.2 and x = -1.6.