Answer:
Given that `x^2 : (20 - 3x) = 1:2`, we can solve for possible values of x as follows:
First, we can cross-multiply to obtain the equation `x^2 * 2 = (20 - 3x) * 1`.
Expanding the right-hand side, we get `2x^2 = 20 - 3x`.
Bringing all the terms to one side, we obtain `2x^2 + 3x - 20 = 0`.
This is a quadratic equation, which can be solved using the quadratic formula: `x = (-b ± sqrt(b^2 - 4ac)) / 2a`.
Plugging in the values `a = 2`, `b = 3`, and `c = -20`, we get:
```
x = (-3 ± sqrt(3^2 - 4*2*(-20))) / 4
x = (-3 ± sqrt(169)) / 4
```
Therefore, the possible values of x are `x = (-3 + 13) / 4 = 2` and `x = (-3 - 13) / 4 = -4`.
So, the possible values of x are 2 and -4.
Explanation: