Answer
$y=-\dfrac{1}{2}\pm\dfrac{\sqrt{29}}{2}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
y^2+y-7=0\\
y^2+y=7\\
y^2+y+\left( \dfrac{1}{2} \right)^2=7+\left( \dfrac{1}{2}\right)^2\\
y^2+y+\dfrac{1}{4}=7+\dfrac{1}{4}\\
\left( y+\dfrac{1}{2} \right)^2=\dfrac{29}{4}\\
y+\dfrac{1}{2}=\pm\sqrt{\dfrac{29}{4}}\\
y=-\dfrac{1}{2}\pm\dfrac{\sqrt{29}}{2}
.\end{array}