Solution set of the inequation $x^2-2x\ge 15$ is

The given inequation is $x^2-2x\ge 15$

$\Rightarrow x^2-2x-15\ge 0$

$\iff$     $\left(x-5\right)\left(x+3\right)\ge 0$

$\iff$     $\left(x-\left(-3\right)\right)\left(x-5\right)\ge 0$

$\iff$    either $x\le -3$  or $x\ge 5$

$\iff$    $x\in \left(-\infty ,3\right]\cup \left[5,\infty \right)$

                           $\left(\because Fora<b,(x-a)(x-b)\ge 0\text{iff}\text{either}x\le aorx\ge b\right)$