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

Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $4x^{2} + 4\sqrt{3}x + 3 = 0$.

$A$ rectangular park is to be designed whose breadth is $3\, m$ less than its length. Its area is to be $4\, m^2$ more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude $12\, m$ (see Figure). Find its length and breadth.

Solve the equation $2x^{2}-5x+3=0$ by the method of completing the square.

Find the roots of the quadratic equation $3x^{2}-2\sqrt{6}x+2=0$.

Find the roots of the following quadratic equation by factorisation:
$x^{2}-3x-10=0$