a) \(1+\left(x-2\right)^2=5\)
\(\Leftrightarrow1+\left(x-2\right)^2-4=5-1\)
\(\Leftrightarrow\left(x-2\right)^2=4\)
\(\Rightarrow\orbr{\begin{cases}x=4\\x=0\end{cases}}\)
b) \(2^0+2^1+3x=5-x\)
\(\Leftrightarrow3x+3=5-x\)
\(\Leftrightarrow3x+3-3=5-x-3\)
\(\Leftrightarrow3x=-x+2\)
\(\Leftrightarrow3x+x=-x+2+x\)
\(\Rightarrow x=\frac{1}{2}\)