To solve the equation 2.4x - 0.25/x - 0.05 = 1.2, we can start by simplifying the equation.

First, let's get rid of the decimal by multiplying the entire equation by 100:

100 * (2.4x - 0.25/x - 0.05) = 100 * 1.2

240x - 25/x - 5 = 120

Next, let's get rid of the fraction by multiplying the entire equation by x:

x * (240x - 25/x - 5) = x * 120

240x^2 - 25 - 5x = 120x

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

240x^2 - 120x - 5x - 25 = 0

240x^2 - 125x - 25 = 0

Now, we can solve this quadratic equation. However, it does not factor easily, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 240, b = -125, and c = -25. Plugging these values into the quadratic formula:

x = (-(-125) ± √((-125)^2 - 4 * 240 * -25)) / (2 * 240)

Simplifying:

x = (125 ± √(15625 + 24000)) / 480

x = (125 ± √39625) / 480

x = (125 ± 199.06) / 480

Now, we have two possible solutions:

x1 = (125 + 199.06) / 480 ≈ 0.77
x2 = (125 - 199.06) / 480 ≈ -0.15

Therefore, the solutions to the equation 2.4x - 0.25/x - 0.05 = 1.2 are approximately x = 0.77 and x = -0.15.