Given equation is,
On cross-multiplying, we get
7(-12x) = 48(x2 – 9)
⇒ -84x = 48x2 – 432
⇒ 48x2 + 84x – 432 = 0
⇒ 4x2 + 7x – 36 = 0 [dividing by 12]
⇒ 4x2 + 16x – 9x – 36 = 0
⇒ 4x(x + 4) – 9(x – 4) = 0
⇒ (4x – 9)(x + 4) = 0
Now, either 4x – 9 = 0 ⇒x = \(\frac{9}{4}\)
Or, x + 4 = 0 ⇒ x = -4
Thus, the roots of the given quadratic equation are x = \(\frac{9}{4}\) and -4 respectively.