Solve the following equations for x:

Given:-

Take

LHS

We know that, Formula

Thus,

⇒

⇒

⇒

⇒

⇒ 62x = 8 – 8x^{2}+ 8

⇒ 4x^{2} + 62x – 16 = 0

⇒ 6x^{2} + 31x – 8 = 0

⇒ 4x(x + 8) – 1(x + 8) = 0

⇒ (4x – 1)(x + 8) = 0

⇒ 6x + 1 = 0 or x – 1 = 0

⇒

Since,

So,

is the root of the given equation

Therefore,

3