Expert Answers

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Divide whole equation by `x^2` (we can do this because `x=0` is obviously not a solution). 


Now we make substitution `y=x+1/x` but first we regroup the terms of the equation.




Now we can use quadratic formula.




Now we return to our substitution.

For `y_2` we get


`(x^2+1)/x=5+sqrt26`  ` `

Multiply by `x.`


Apply quadratic equation.





`x_1` and `x_2` are first two solutions. 

Now we put `y_1` into our substitution.




Apply quadratic formula.


`x_3=(5-sqrt26-i sqrt(10sqrt26-47))/2` <-- Third solution 

`x_4=(5-sqrt26+isqrt(10sqrt26-47))/2`  <-- Fourth solution

Solutions of the equation are `x_1,x_2,x_3,x_4.`

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