Answer:
[tex]x=\frac{1}{2}[/tex] or [tex]x=2[/tex]
Step-by-step explanation:
The given quadratic equation is:
[tex]\frac{4}{5}x^2=2x-\frac{4}{5}[/tex]
We multiply through by 5 to get:
[tex]4x^2=10x-4[/tex]
Rewrite in standard quadratic form;
[tex]4x^2-10x+4=0[/tex]
Or
[tex]2x^2-5x+2=0[/tex]
Split the middle term to get:
[tex]2x^2-4x-x+2=0[/tex]
Factor to get:
[tex]2x(x-2)-1(x-2)=0[/tex]
Factor further to get:
[tex](2x-1)(x-2)=0[/tex]
Either [tex](2x-1)=0[/tex] or [tex](x-2)=0[/tex]
Either [tex]x=\frac{1}{2}[/tex] or [tex]x=2[/tex]
