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

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Solution

$(x - 3) (2 x + 1) = x (x - 5)$
$\Rightarrow$ $2 x^{2} + x - 6 x - 3 = x^{2} - 5 x$
$\Rightarrow$ $2 x^{2} + x - 6 x - 3 - x^{2} + 5 x = 0$
$\Rightarrow$ $x^{2} - 3 = 0$
$\Rightarrow$ A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared
$\Rightarrow$ Comparing given equation with standard form of quadratic equation $a x^{2} + b x + c = 0.$
$\Rightarrow$ We get, $a = 1, b = 0, c = 3$
$∴$ Given equation is quadratic equation

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