Solve the following equation by using the general formula,if the equation has a solution in $R$: $5x^{2} + 12x + 10 = 0$.

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

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.

Is the following situation possible? If so,determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago,the product of their ages in years was $48$.

The formula for finding the value of $D$ (discriminant) for a quadratic equation $ax^2 + bx + c = 0$ is $\ldots \ldots \ldots \ldots.$

Which of the following equations has the sum of its roots as $3$?