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

$A$ train travels at a certain average speed for a distance of $63 \, km$ and then travels a distance of $72 \, km$ at an average speed of $6 \, km/h$ more than its original speed. If it takes $3 \, hours$ to complete the total journey,what is its original average speed in $km/h$?

Which of the following is a quadratic equation?

If $64$ is the discriminant of $k x^{2}-4 x-4=0$,then the value of $k$ is ...........

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $3x^{2} + x - 2 = 0$.

State whether the quadratic equation $3 x^{2}-4 x+1=0$ has two distinct real roots. Justify your answer.