Question

Solve:
$2y+\frac{11}{4}=\frac{1}{3y}+2$

Answer 1

$2y+\frac{11}{4}=\frac{1}{3y}+2$

$\Rightarrow \frac{8y+11}{4}=\frac{1+6y}{3y}$

$\Rightarrow 24y^2+33y=24y+4$

$\Rightarrow 24y^2+9y-4=0$

$\Rightarrow y=\frac{-9\pm \sqrt{81+16\left(24\right)}}{48}=\frac{-9\pm \sqrt{81+38y}}{48}=\frac{-9\pm \sqrt{465}}{48}$

$\Rightarrow y=\frac{-9\pm \sqrt{465}}{48}$.