$$b^4-2b^2+1+3b^2-2b+3 = 0$$
Answer
$$ \begin{matrix}b_1 = 0.88818+0.852i & b_2 = 0.88818-0.852i & b_3 = -0.88818+1.36081i \\[1 em] b_4 = -0.88818-1.36081i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} b^4-2b^2+1+3b^2-2b+3 &= 0&& \text{simplify left side} \\[1 em]b^4+b^2-2b+4 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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