To solve this equation, we first need to simplify the expression:

2(x^2 + 25/x^2) + 21(x + 5/x) + 74 = 0

Expanding the terms inside the parentheses:

2x^2 + 50/x^2 + 21x + 105/x + 74 = 0

Now, we can combine like terms:

2x^2 + 21x + 50/x^2 + 105/x + 74 = 0

To simplify further, we can multiply through by x^2 to get rid of the fractions:

2x^4 + 21x^3 + 50 + 105x + 74x^2 = 0

Rearranging the terms:

2x^4 + 21x^3 + 74x^2 + 105x + 50 = 0

This is a quartic equation, which can be difficult to solve. You may need to use numerical methods or a graphing calculator to find the roots of this equation.