The equation to be solved is 6a^-2 + a^-1 = 2

6a^-2 + a^-1 = 2

Let a^-1 = y

=> 6y^2 + y = 2

=> 6y^2 + y - 2 = 0

=> 6y^2 + 4y - 3y - 2 = 0

=> 2y(3y + 2) - 1(3y + 2) = 0

=> (2y - 1)(3y + 2) = 0

2y - 1 = 0

=> y = 1/2

=> a^-1 = 1/2

=> 1/a = 1/2

=> a = 2

3y + 2 = 0

=> y = -2/3

=> a^-1 = -2/3

=> 1/a = -2/3

=> a = -3/2

**The solution of the equation is a = 2 and a = -3/2**

The value of a has to be determined given that 6a^-2 + a^-1 = 2

Note that the exponent of a^-2 is twice that of a^-1. It is possible to convert 6a^-2 + a^-1 = 2 into a quadratic equation.

6a^-2 + a^-1 = 2

Let x = a^-1.

6x^2 + x = 2

6x^2 + x - 2 = 0

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

2x(3x + 2) - 1(3x + 2) =0

(2x - 1)(3x +2) = 0

x = 1/2 and x = -2/3

Now x = a^-1

a = 2 and a = -1.5

The equation 6a^-2 + a^-1 = 2 has solution a = 2 and a = -1.5