Explanation

(c)
We have,
$\sqrt{3x^{2} - 7x - 30} + \sqrt{2x^{2} - 7x - 5} = x + 5$
$\Rightarrow \sqrt{3x^{2} - 7x - 30} = (x + 5) - \sqrt{2x^{2} - 7x - 5}$
On squaring both sides, we get
$3x^{2} - 7x - 30 = x^{2} + 25 + 10x + \left( 2x^{2} - 7x - 5 \right) - 2(x + 5)\sqrt{2x^{2} - 7x - 5}$
$\Rightarrow \ \sqrt{2x^{2} - 7x - 5}$=5
Again on squaring both sides, we get
$2x^{2} - 7x - 30 = 0$
$\Rightarrow x = 6$