Verified answer

6x^−2 = 6 / x^2 and x^−1 = 1 / x --> (negative indicies put into fraction as positive indices in denominator)

so,

6/x^2 + 1/x = 2

(cross multiply)

x^2 + 6x = 2

x^2 + 6x - 2 = 0 --> so now its a quadratic

6x^−2 + x^−1 = 2

(6/x^2) + 1/x = 2

Multiply each term with x^2

6 + x = 2x^2

Reassembling the equation,

2x^2 - x - 6 = 0

2x^2 - 4x + 3x - 6 = 0

2x (x-2) + 3 (x-2) = 0

(2x+3) (x-2) = 0

Thus, either (2x+3) = 0 or (x-2) = 0

So, x = (-3/2) or x = 2

Hence the solution.