If $-3$ is a solution of $2x^{2} + 5x + k = 0$,then $k = \ldots$

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

Verify whether the given value of $x = 2$ is a solution of the quadratic equation $\frac{1}{x+4} - \frac{1}{x-7} = \frac{11}{30}$ or not.

Find the roots of the following quadratic equation by the method of completing the square: $4x^{2} + 20x + 23 = 0$.

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

Examine whether the following equation is quadratic or not: $(x-3)(2x+1) = x(x+5)$