How to solve for $t$ in $16((t^2-2)^2-2)-4(t^2-2)-2t=235$?

Question

How can I solve for $t$ in $$16((t^2-2)^2-2)-4(t^2-2)-2t=235$$
?

Can I solve it somehow like a quadratic equation?

N.B. In the equation I need to solve, $t$ is given by $t\equiv 2^\frac{x}{4}+\frac{1}{2^\frac{x}{4}}$.

Answer 1

You can expand to $$16 t^4 - 68 t^2 - 2 t - 195 = 0$$

and look for rational roots by Rational root theorem. Once you find a root you can factor to a cubic.

A an alternative you can solve completely by the general solution Quartic Equation