Answer
$\left\{ \dfrac{1-\sqrt{57}}{8},\dfrac{1+\sqrt{57}}{8} \right\}$
Work Step by Step
The standard form of the given equation, $
8m^2-2m=7
,$ is
\begin{array}{l}\require{cancel}
8m^2-2m-7=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
8m^2-2m-7=0
,$ are
\begin{array}{l}\require{cancel}
\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{2\pm\sqrt{4\cdot57}}{16}
\\\\=
\dfrac{2\pm\sqrt{(2)^2\cdot57}}{16}
\\\\=
\dfrac{2\pm2\sqrt{57}}{16}
\\\\=
\dfrac{2(1\pm\sqrt{57})}{16}
\\\\=
\dfrac{\cancel{2}(1\pm\sqrt{57})}{\cancel{2}\cdot8}
\\\\=
\dfrac{1\pm\sqrt{57}}{8}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{1-\sqrt{57}}{8},\dfrac{1+\sqrt{57}}{8} \right\}
.$
