Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $9x^2 + 6x + 4 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} = 9$.

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

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)

If the roots of the quadratic equation $5x(2x - 3) - 4 = 0$ exist,find them using the method of completing the square.

If the roots of the following quadratic equation exist,find them by the method of completing the square: $3x^2 + 7x + 5 = 0$.