ĐK: `x>=-4/3`
`(x+1)(x+4)+2=2\sqrt{3x+4}`
`<=>x^2+5x+4+2=2\sqrt{3x+4}`
`<=>x^2+5x+6-2\sqrt{3x+4}=0`
`<=>(x^2+2x+1)+(3x+4-2\sqrt{3x+4}+1)=0`
`<=>(x+1)^2+(\sqrt{3x+4}-1)^2=0`
`<=>`\(\left[ \begin{array}{l}x+1=0\\3x+4=1\end{array} \right.\)
`<=>x=-1\ \ (TM)`
Vậy phương trình có nghiệm `x=-1`