If $\ldots \ldots \ldots$ then real roots of a quadratic equation do not exist.

Find the discriminant of the following quadratic equation: $x^{2}+2x-2=0$.

Examine whether the following equation is quadratic or not: $x(x+1)+8=(x+2)(x-2)$

Examine whether the following equation is quadratic or not: $(x-3)(2x+1) = x(x+5)$

Which of the following equations has the sum of its roots as $3$?

The length of a rectangular garden exceeds its breadth by $6 \, m$. If the area of the garden is $216 \, m^2$,find the length and the breadth of the garden.