Answer
The solution is $x=2\pm\sqrt{6}$
Work Step by Step
$(2x+1)(x-4)=x$
Evaluate the product on the left side:
$2x^{2}-8x+x-4=x$
Take $x$ to the left side and simplify:
$2x^{2}-8x+x-4-x=0$
$2x^{2}-8x-4=0$
Divide the whole equation by $2$:
$\dfrac{1}{2}(2x^{2}-8x-4=0)$
$x^{2}-4x-2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=1$, $b=-4$ and $c=-2$.
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-4)\pm\sqrt{(-4)^{2}-4(1)(-2)}}{2(1)}=\dfrac{4\pm\sqrt{16+8}}{2}=...$
$...=\dfrac{4\pm\sqrt{24}}{2}=\dfrac{4\pm2\sqrt{6}}{2}=\dfrac{4}{2}\pm\dfrac{2\sqrt{6}}{2}=2\pm\sqrt{6}$
The solution is $x=2\pm\sqrt{6}$
