#### Answer

$x=-\dfrac{1}{14}\pm\dfrac{\sqrt{57}}{14}$

#### Work Step by Step

$x(7x+1)=2$
Evaluate the product on the left side of the equation:
$7x^{2}+x=2$
Take the $2$ to the left side of the equation:
$7x^{2}+x-2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=7$, $b=1$ and $c=-2$.
Substitute:
$x=\dfrac{-1\pm\sqrt{1^{2}-4(7)(-2)}}{2(7)}=\dfrac{-1\pm\sqrt{1+56}}{14}=...$
$...=\dfrac{-1\pm\sqrt{57}}{14}=-\dfrac{1}{14}\pm\dfrac{\sqrt{57}}{14}$