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

Represent the following situation in the form of a quadratic equation:
The area of a rectangular plot is $528 \ m^{2}$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Check whether the following is a quadratic equation:
$(2x - 1)(x - 3) = (x + 5)(x - 1)$

In a class test,the sum of Shefali's marks in Mathematics and English is $30$. Had she got $2$ marks more in Mathematics and $3$ marks less in English,the product of their marks would have been $210$. Find her marks in the two subjects.

Find the roots of the following equation:
$\frac{1}{x} - \frac{1}{x-2} = 3, x \neq 0, 2$

Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $2x^2 - 7x + 3 = 0$.