Check whether the following is a quadratic equation:
$(x+1)^{2}=2(x-3)$

Represent the following situation in the form of a quadratic equation:
Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan's present age.

Represent the following situation mathematically:
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 $124$. We would like to find out how many marbles they had to start with.

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $x^{2}+4x+5=0$.

Find the roots of the equation $5x^{2}-6x-2=0$ by the method of completing the square.

Check whether the following is a quadratic equation:
$(x-2)(x+1)=(x-1)(x+3)$