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

Which of the following is true for the coefficients and constant term of a quadratic equation $ax^2 + bx + c = 0$?

Obtain the roots of the following quadratic equation by using the quadratic formula: $6x^{2} + x - 2 = 0$.

The speed of a motorboat in still water is $9\,km/h$. In a river,it covers $12\,km$ downstream and the same distance upstream in a total time of $3\,hours$. Find the speed of the current of the river. (The speed of the current of the river is less than the speed of the motorboat in still water.) (in $,km/h$)

The roots of a quadratic equation $x^{2} = 49$ are ..... .

While selling a calculator for Rs. $56$,the profit percentage is equal to its cost price in rupees. Find the cost price of the calculator.