Solve the following equation using the method of factorization: $x + 3 + \frac{2}{x} = 0$.

Find the roots of the quadratic equation $6x^{2}-x-2=0$.

$A$ cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was $3$ more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ $90,$ find the number of articles produced and the cost of each article.

Find the roots of the following quadratic equation by the method of completing the square: $m^{2}-18m+81=0$

If the roots of the quadratic equation $x(x+1)-6=0$ are

John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each,and the product of the number of marbles they now have is $124$. Find out how many marbles they had to start with.