Check whether the following is quadratic equation.
$x^{2} - 2 x = (- 2) (3 - x)$

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Solution

$x^{2} - 2 x = (- 2) (3 - x)$
$\Rightarrow$ $x^{2} - 2 x = - 6 + 6 x$
$\Rightarrow$ $x^{2} - 2 x - 6 x + 6 = 0$
$\Rightarrow$ $x^{2} - 8 x + 6 = 0$
$\Rightarrow$ A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
$\Rightarrow$ Comparing given equation $x^{2} - 8 x + 6 = 0$ with standard form of quadratic equation $a x^{2} + b x + c = 0.$
$\Rightarrow$ We get, $a = 1, b = - 8, c = 6$
$∴$ Given equation is quadratic equation.

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