Answer
$-\frac{1}{4},\frac{2}{3}$,
$(-\frac{1}{4},\frac{25}{16})$,
$(\frac{2}{3},-\frac{10}{9})$.
Work Step by Step
Step 1. Let $f(x)=g(x)$ to get $5x^2-5x=-7x^2+2 \longrightarrow 12x^2-5x-2=0 \longrightarrow (3x-2)(4x+1)=0 \longrightarrow x=-\frac{1}{4},\frac{2}{3}$
Step 2. For $x=-\frac{1}{4}$, we have $g(-\frac{1}{4})=-7(-\frac{1}{4})^2+2=\frac{25}{16}$ or intersect $(-\frac{1}{4},\frac{25}{16})$,
Step 3. For $x=\frac{2}{3}$, we have $g(\frac{2}{3})=-7(\frac{2}{3})^2+2=-\frac{10}{9}$ or intersect $(\frac{2}{3},-\frac{10}{9})$.
