Answer:
Step-by-step explanation:
First, rewrite the equation (all terms should be in the left side):
[tex]5y^2-8y-2=0.[/tex]
In this equation,
- [tex]a=5;[/tex]
- [tex]b=-8;[/tex]
- [tex]c=-2.[/tex]
Then the discriminant
[tex]D=b^2 -4ac=(-8)^2-4\cdot 5\cdot (-2)=64+40=104.[/tex]
Then
[tex]y_1=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-(-8)+\sqrt{104}}{2\cdot 5}=\dfrac{8+2\sqrt{26}}{10}=\dfrac{4+\sqrt{26}}{5},\\ \\y_2=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-(-8)-\sqrt{104}}{2\cdot 5}=\dfrac{8-2\sqrt{26}}{10}=\dfrac{4-\sqrt{26}}{5}.[/tex]
