4x(5x-2) + 9.6 = 2x(2+x)

Expanding both sides:

20x^2 - 8x + 9.6 = 4x + 2x^2

Combining like terms:

18x^2 - 12x + 9.6 = 6x^2

Rearranging terms:

12x^2 - 12x - 9.6 = 0

Dividing by 1.2 to simplify:

10x^2 - 10x - 8 = 0

Now, you can solve for x using the quadratic formula:

x = [-(-10) ± sqrt((-10)^2 - 4(10)(-8))] / 2(10)
x = [10 ± sqrt(100 + 320)] / 20
x = [10 ± sqrt(420)] / 20
x = [10 ± 20.5] / 20

x = 1.025 or x = -0.775

Therefore, the solutions for x are 1.025 and -0.775.