Find the discriminant of the following quadratic equation: $x^{2}-5x-14=0$.

Find the roots of the following quadratic equation by the method of completing the square: $2x^{2} - 7x + 3 = 0$.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4}; \, x \neq -1, -2, -4$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $(k+1) x^{2}-2(k+3) x+(2 k+3)=0$

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2}-6x+2=0$.

Find the roots of the quadratic equation by using the quadratic formula: $-x^{2}+7x-10=0$.