$\\$
`d,`
`(2x+3)^2 = 4 (x^2 + 6)`
`⇔ 4x^2 + 12x + 9 =4x^2 + 24`
`⇔ 4x^2 +12x + 9 -4x^2 - 24=0`
`⇔ 12x-15=0`
`⇔ 12x=15`
`⇔x=15/12`
Vậy `x=15/12`
$\\$
`e,`
`(4x+1)^2=5(3x^2+1)`
`⇔ 16x^2 + 8x + 1 = 15x^2 + 5`
`⇔ 16x^2 + 8x + 1 - 15x^2 - 5=0`
`⇔ x^2 + 8x - 4=0`
`⇔ x^2 + 2 . x . 4 + 4^2 - 20=0`
`⇔ (x+4)^2=20`
`⇔` \(\left[ \begin{array}{l}(x+4)^2=(\sqrt{20})^2\\(x+4)^2=(-\sqrt{20})^2\end{array} \right.\) $\\$ `<=>` \(\left[ \begin{array}{l}x+4=\sqrt{20}\\x+4=-\sqrt{20}\end{array} \right.\) $\\$ `<=>` \(\left[ \begin{array}{l}x=-4+2\sqrt{5}\\x=-4-2\sqrt{5}\end{array} \right.\)
Vậy `x=-4+2\sqrt{5}, x=-4-2\sqrt{5}`
