Rearrange the formula as
[tex] x^4 +3x^2-4=0 [/tex]
Define [tex] t=x^2 [/tex] so that the equation becomes a quadratic one:
[tex] t^2+3t-4=0 [/tex]
Use the quadratic formula to solve this:
[tex] t_{1,2} = \dfrac{-3\pm\sqrt{9+16}}{2} = \dfrac{-3\pm 5}{2} [/tex]
Which implies
[tex] t=\dfrac{-3-5}{2} =-4 \text{ or } t = \dfrac{-3+5}{2} = 1 [/tex]
Now, remember that [tex] t=x^2 [/tex]
So, the solutions in t translate as
[tex] t=-4 \implies x^2=-4 \iff x=\pm 2i,\quad t=1 \implies x^2=1 \iff x=\pm 1 [/tex]
