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

Examine whether the following equation is quadratic or not: $(x+2)^{3} = x(x^{2}-1)$

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 quadratic equation by using the quadratic formula:
$\frac{1}{2} x^{2}-\sqrt{11} x+1=0$

Which of the following is a quadratic equation?

Which one of the following is not a quadratic equation?