Answer:
[tex]x\in\left\{\dfrac{1+\sqrt{11}}{5}\,;\ \dfrac{1-\sqrt{11}}{5}\right\}[/tex]
Step-by-step explanation:
[tex]-5y^2+2y=-2\\\\-5y^2+2y+2=0\\\\a=-5\,,\ \ b=2\,,\ \ c=2\\\\\Delta=2^2-4\cdot(-5)\cdot2=44\quad\implies\quad\sqrt\Delta=2\sqrt{11}\\\\x_1=\dfrac{-2-2\sqrt{11}}{2\cdot(-5)}=\dfrac{-2(1+\sqrt{11})}{-2\cdot5}=\dfrac{1+\sqrt{11}}{5}\\\\x_2=\dfrac{-2+2\sqrt{11}}{2\cdot(-5)}=\dfrac{-2(1-\sqrt{11})}{-2\cdot5}=\dfrac{1-\sqrt{11}}{5}[/tex]
