What is the number $\;'c'\;$ that satisfies the conclusion of Rolle's theorem? I have a problem
What is the number $\;'c'\;$ that satisfies the conclusion of Rolle's theorem for the function $$f(x)=(x^2-1)(x-2)\;\;\text{in}\;(1,\;2]$$
I've tried$$f'(x)= 3x^2-4x-1$$
we know,  to fiind 'c' $$f'(x)=0$$
So, $$\Rightarrow 3x^2-4x-1=0\\x=\dfrac {4+ \sqrt 4}{6}=1\\ x=\dfrac {4- \sqrt 4}{6}=0.33\\\therefore 1\notin(1,\;2]\\0.33\notin(1,\;2]$$
Please help. Where I've made misstake.

Solve quadratic equation correctly
$$3x^2-4x-1=0\\\Rightarrow \dfrac{4\pm\sqrt{16-4(3)(-1)}}{2(3)}\\\Rightarrow x=\dfrac {2\pm \sqrt 7}{3}\\\Rightarrow x=\dfrac {2+ \sqrt 7}{3}\;\text{and}\; x=\dfrac {2- \sqrt 7}{3}\\x=\dfrac {2+ \sqrt 7}{3}=1.55\in (1,\;2]\\ x=\dfrac {2- \sqrt 7}{3}=-.215\notin(1,\;2]$$
Hence, 
$\; c=\dfrac {2+ \sqrt 7}{3}\;$  satisfies the conclusion of Rolle's theorem for the given function.
