To solve this equation, we first need to find a common denominator for the terms involving x and 1/x.

Multiplying the entire equation by x^2, we get:

x^4 +1 + x^2 + x = 29x/10

Now, let x = y, we have:

y^4 + 1 + y^2 + y = 29y/10

Rearranging the terms to one side of the equation, we get:

y^4 + y^2 + y - 29y/10 + 1 = 0

Multiplying by 10 to clear the fraction, we get:

10y^4 + 10y^2 + 10y - 29y + 10 = 0

10y^4 + 10y^2 - 19y + 10 = 0

Now, we can use a numerical method or a solver to find the roots of this equation. Alternatively, we can use a CAS calculator to solve it.