Find the roots (real or complex) of the equation 2a2(1+cos⁡x)−(1+a2+b2)2=0,a,b∈R ATTEMPT: Solving for x, we...

Find the roots (real or complex) of the equation ${\displaystyle 2a^2(1+\cos x)-{(1+a^2+b^2)}^2=0,a,b\in \mathbb{R}}$
ATTEMPT: Solving for x, we arrived with
${\displaystyle x=\arccos [\frac{{(1+a^2+b^2)}^2}{2a^2}-1]}$
However, I got stuck because of the required domain of ${\displaystyle \arccos (\cdot )}$ which is [-1,1] while the expression ${\displaystyle \frac{{(1+a^2+b^2)}^2}{2a^2}-1}$ does not possibly be within this interval for arbitrary values of a and b. Sometimes I am tempted to say that no general solution exists even in C. Can anyone help me out?