Answer
$m=\dfrac{1}{8}\pm\dfrac{\sqrt{57}}{8}$
Work Step by Step
$8m^{2}-2m=7$
Take the $7$ to the left side of the equation:
$8m^{2}-2m-7=0$
Use the quadratic formula to solve this equation. The formula is $m=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=8$, $b=-2$ and $c=-7$
Substitute:
$m=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(8)(-7)}}{2(8)}=\dfrac{2\pm\sqrt{4+224}}{16}=...$
$...=\dfrac{2\pm\sqrt{228}}{16}=\dfrac{1}{8}\pm\dfrac{\sqrt{57}}{8}$
