Examine whether the following equation is quadratic or not: $x - \frac{1}{x} = 5$

Solve the following quadratic equation using the quadratic formula,if the equation has a solution in $R$: $3x^2 + 5\sqrt{2}x - 2 = 0$.

$A$ natural number,when increased by $12$,equals $160$ times its reciprocal. Find the number.

The speed of a motor-boat in still water is $x \, km/hr$ and the speed of the current of the river is $5 \, km/hr$. Given $x$ > 5, what is the time taken to cover a distance of $y \, km$ upstream?

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

If Zeba were younger by $5\, \text{years}$ than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now? (in $\text{years}$)