The roots of a quadratic equation $6 x^{2}-13 x+6=0$ are .... .

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^{2} - 6x + 3 = 0$; $x = \frac{1}{2}$.

Obtain the roots of the following quadratic equation by using the quadratic formula: $9x^{2} + 7x - 2 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 11x + 10 = 0$

$A$ two-digit number is such that the product of its digits is $6$. When $9$ is subtracted from the number,the resulting number is the number obtained by interchanging the digits. Find the original number.

Examine whether the following equation is quadratic or not: $(2x + 1)(3x + 2) = 6(x - 1)(x - 2)$