Are these really quadratic equations? (2/3)x^2 - (2/3)x = 0 and 6x^2 - 1 = 0

[chijioke]

What you have posted for the first equation differs (significantly) from your picture!

While you posted:- [math].~~\frac{2}{3}x-\frac{2}{3}x=0[/math]Your picture shows:- [math]6  \frac{2}{3}x^2-\frac{2}{3}x=0[/math]
But:- [math]\frac{2}{3}x^2-\frac{2}{3}x=0   \Rightarrow  \frac{2}{3}x^2-\frac{2}{3}x +0=0[/math]and
[math]6x^2-1=0   \Rightarrow  6x^2+0x-1=0[/math]
Does that resolve your "difficulty"?

See also @blamocur's comment(s) above. (Posted while I was 'composing' this response. ?)

Difficulty resolved.