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

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\frac{1}{3-2x} + \frac{1}{5+2x} = \frac{1}{2}$; $x = -\frac{1}{2}$.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\sqrt{3}x^{2} - 2x + \sqrt{3} = 0$

Find the roots of the following quadratic equation by the method of completing the square: $4x^{2} + 4bx - (a^{2} - b^{2}) = 0$.

Solve the following equation by using the quadratic formula,if the equation has a solution in $R$: $x^{2}-3x-4=0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x(x - 5) = 36$.