To solve the equation, we need to simplify and then isolate x.

First, simplify the equation by combining like terms:

(2x^2/5) - (4x - 2/3) = -0.2
(2x^2/5) - 4x + 2/3 = -0.2

Next, get rid of the fraction by multiplying everything by 15 (the least common multiple of 5 and 3):

15(2x^2/5) - 15(4x) + 15(2/3) = 15(-0.2)
6x^2 - 60x + 10 = -3

Now, rearrange the equation to get it in standard form:

6x^2 - 60x + 10 + 3 = 0
6x^2 - 60x + 13 = 0

Finally, solve for x using the quadratic formula:

x = (-(-60) ± √((-60)^2 - 4(6)(13)))/(2(6))
x = (60 ± √(3600 - 312))/12
x = (60 ± √3288)/12
x ≈ (60 ± 57.34)/12
x ≈ (117.34/12) or x ≈ (2.66/12)

Therefore, the solutions for x are approximately x ≈ 9.78 or x ≈ 0.22.