\(\Leftrightarrow4x+1+x+1+\sqrt{4\left(4x+1\right)\left(x+1\right)}=4x^2+4x+1\)
\(\Leftrightarrow\sqrt{4\left(4x+1\right)\left(x+1\right)}=4x^2-x-1\)
\(\Leftrightarrow4\left(4x+1\right)\left(x+1\right)=\left(4x^2-x-1\right)^2\)
\(\Leftrightarrow16x^4+x^2+1-8x^3-8x^2+2x-4\left(4x^2+5x+1\right)=0\)
\(\Leftrightarrow16x^4-8x^3-7x^2+2x+1-16x^2-20x-4=0\)
=>\(16x^4-8x^3-23x^2-18x-3=0\)
\(\Leftrightarrow x\in\left\{-0,22;1,74\right\}\)
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