Solve the following equation by using formula : 2 x+5 3 x+4 =x+1 … - Vidyadip

Question

Solve the following equation by using formula :
$
\frac{2 x+5}{3 x+4}=\frac{x+1}{x+3}
$

✓

Answer

$\begin{aligned} & \frac{2 x+5}{3 x+4}=\frac{x+1}{x+3} \\ & (2 x+5)(x+3)=(x+1)(3 x+4) \\ & 2 x^2+6 x+5 x+15=3 x^2+4 x+3 x+4 \\ & \Rightarrow 3 x^2+7 x+4-2 x^2-11 x-15=0 \\ & \Rightarrow x^2-4 x-11=0 \\ & \text { Here } a=1, b=-4, c=-11 \\ & D=b^2-4 a c \\ & =(-4)^2-4 x 1 x(-11) \\ & =16+44 \\ & =60 \\ & \because x=\frac{-b \pm \sqrt{D}}{2 a} \\ & =\frac{-(-4) \pm \sqrt{60}}{2 \times 1} \\ & =\frac{4 \pm \sqrt{4 \times 15}}{2} \\ & =\frac{4 \pm 2 \sqrt{15}}{2} \\ & =2 \pm \sqrt{15} \\ & \therefore x=2+\sqrt{15}, 2-\sqrt{15} .\end{aligned}$

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