Question

Solve:
$\frac{2x-1}{x+4}-2x-5x+3=0$

Answer 1

$\frac{2x-1}{x+4}-2x-5x+3=0$

$\Rightarrow \frac{2x-1}{x+4}-7x+3=0$

$\Rightarrow \frac{2x-1-(7x-3)(x+4)}{x+4}=0$

$\Rightarrow 2x-1-7x^2-28x+3x+12=0$

$\Rightarrow 7x^2+23x-11=0$

Here $a=7,b=23,c=-11$

Now, by quadratic formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow x=\frac{-23\pm \sqrt{{\left(23\right)}^2-4\cdot 7\cdot (-11)}}{2\times 7}$

$\Rightarrow x=\frac{-23\pm \sqrt{529+308}}{14}$

$\Rightarrow x=\frac{-23\pm \sqrt{837}}{14}$

$\Rightarrow x=\frac{-23\pm 3\sqrt{93}}{14}$