Question: In $(X,d)$ metric space, If $\{x\_n\}\_{n\in\Bbb N}$ and $\{y\_n\}\_{n\in\Bbb N}$ are two sequences which converge to the same point, then prove that

$$\lim\_{n\to\infty} d(x\_n,y\_n)=0$$

This question is found in the chapter of completeness, but I could not figure out where to use completeness for this question.

Answer: 
$$6x^2-19x+10=0$$
$$6x^2-15x-4x+10=0$$
$$3x(2x-5)-2(2x-5)=0$$
$$(3x-2)(2x-5)=0$$

Hope it helps?

For your second format, you can write it as:

$$10x^2-5x-4x+2=0$$
and proceed
\begin{align}6x^2−19x+10=0\\ 
6x^2−15x−4x+10=0\\ 
3x(2x−5)−2(2x−5)=0\\ 
(3x−2)(2x−5)=0\end{align}

Now for the above equation to be equal to zero, either $(3x-2)$ needs to be equal to zero or $(2x-5)$ needs to be equal to zero.They both can also be equal to zero. So,

$3x-2=0$  

$x=2/3$ 

Similarly, $x$ can also be equal to $5/2$. 

For your second problem, you can rewrite it as 

\begin{align}10x^2−5x−4x+2=0\end{align}

Can you take it from here?