To solve this quadratic equation, we first need to expand the expression on the left side of the equation.

(х-2)(х+2)+2х^2 = 0.96

Multiplying out (х-2)(х+2) using the distributive property, we get:

х^2 + 2х - 2х - 4 + 2х^2 = 0.96

Combining like terms, we get:

3х^2 - 4 = 0.96

Next, we'll add 4 to both sides of the equation to isolate the quadratic term:

3х^2 = 4.96

Then, we'll divide both sides by 3 to solve for х^2:

х^2 = 1.65333

Finally, we'll take the square root of both sides to solve for х:

х ≈ ±1.286

Therefore, the solutions to the quadratic equation are approximately х = 1.286 and х = -1.286.