One 2 Class Example and multiple choice question answer different?

Question

I select one example from my notes (this is multiple choice) as follows:

Question and Parameters attached to my solution is present as following image:

but when I plot these as the interval of $x$ is differ from above calculation, why?

and the answer option of multiple choice for this question is quite differ:

Answer 1

You started working with the assumption that $ 0 \le x \le 1$.

Notice that $\frac{8-\sqrt{76}}2 < 0$ and $\frac{8 + \sqrt{76}}2 > 1$.

$$\left[ \frac{8-\sqrt{76}}{2}, \frac{8+\sqrt{76}}{2} \right] \cap [0,1]=[0,1]$$