The polynomial: $8x^4-8x^2+1=\frac{\sqrt{3}}{2}$
I can simplify with $u=x^{2}$ to $8u^2-8u+{\frac{\sqrt{3}}{2}}=0$ Mistake $\left(1-\frac{\sqrt{3}}{2}\right)$
apply the quadratic formula: $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\frac{-(-8)\pm\sqrt{(-8)^2-4(8)\frac{\sqrt{3}}{2}} } {2a}$
reduces to: $u=1\pm \frac{\sqrt{64-16\sqrt{3}}}{2}$
That is what I have done. then I just take the square root of each value of u, and that will give me all 4 values?
I checked my result with wolfalpha. I don't understand why when it say completing the square did it add $1/4$ and not $\left(\frac{-b}{2}\right)$?