Check whether the following is a quadratic equation:
$(2x - 1)(x - 3) = (x + 5)(x - 1)$

Represent the following situation in the form of a quadratic equation:
Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan's present age.

$A$ cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be $55$ minus the number of toys produced in a day. On a particular day,the total cost of production was $Rs$ $750$. Find out the number of toys produced on that day.

Find the discriminant of the equation $3x^{2}-2x+\frac{1}{3}=0$ and hence find the nature of its roots. Find them,if they are real.

Find the nature of the roots of the following quadratic equation. If real roots exist,find them:
$3x^2 - 4\sqrt{3}x + 4 = 0$

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $x^{2}+4x+5=0$.