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

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Solution

$(x - 3) (2 x + 1) = x (x + 5) \Rightarrow 2 x^{2} - 5 x - 3 = x^{2} + 5 x \Rightarrow x^{2} - 10 x - 3 = 0$
It is of the form $a x^{2} + b x + c = 0$ ,where $a = 1, b = - 10, c = - 3$ in this case.
Hence, the given equation is quadratic equation.

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