You want to solve an inequality
16x^2 + 1 >= -8x.
It is equivalent to
16x^2 + 8x + 1 >= 0.
It is equivalent to
>= 0.
The last inequality is valid for all real values x.
Answer. The given inequality has the set of solutions ALL REAL NUMBERS.
Plot y =
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Be aware : The solution by @rapture1965 is I N C O R R E C T.