The function f (x) = 2aX ^ 2 + 4ax + 1 / 3 is defined as R, and the value range of real number a is calculated?

The function f (x) = 2aX ^ 2 + 4ax + 1 / 3 is defined as R, and the value range of real number a is calculated?

F (x) = 2aX ^ 2 + 4ax + 1 / 3, the definition field is r, indicating that 2aX ^ 2 + 4ax + 3 ≠ 0, this quadratic function has no intersection with X axis, that is, this quadratic function has no real number
That is, δ < 0, (4a) ^ 2-4 * 2A * 3