The solution set of $x^{2}+5x+6=0$ is $\ldots \ldots \ldots \ldots.$

Find whether the following equation has real roots. If real roots exist,find them.
$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$

Solve the following equation using the method of 'completing the square': $x^{2}+3x-5=0$.

State whether the quadratic equation $x(1-x)-2=0$ has two distinct real roots. Justify your answer.

The price of corn oil is ₹ $x$ per $kg$. If the price of corn oil is decreased by ₹ $10$ per $kg$,then how many kilograms of corn oil can be obtained for ₹ $500$ at the new rate?

The length of the hypotenuse of an isosceles right-angled triangle is $8 \, cm$. Find the length of the other two sides.