Answer:
[tex]\text{The roots are }\frac{4}{5}\pm \frac{\sqrt{26}}{5}[/tex]
Step-by-step explanation:
Given the equation
[tex]5y^2-8y=2[/tex]
we have to solve the above equation using quadratic formula
[tex]5y^2-8y-2=0[/tex]
[tex]\text{Comparing above equation with the standard equation }ax^2+bx+c=0\text{ , we get}[/tex]
a=5, b=-8, c=-2
By quadratic formula the solution is
[tex]y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]y=\frac{8\pm \sqrt{(-8)^2-4(5)(-2)}}{2(5)}[/tex]
[tex]y=\frac{8\pm \sqrt{104}}{10}[/tex]
[tex]y=\frac{4}{5}\pm \frac{2\sqrt{26}}{10}=\frac{4}{5}\pm \frac{\sqrt{26}}{5}[/tex]
[tex]\text{The roots are }\frac{4}{5}\pm \frac{\sqrt{26}}{5}[/tex]
