Substitute $3$ for each $x$ in $f(x)$.

$f(3)=-\frac{2}{3}(3)+3$

Simplify.

Substitute $−5$ for $f(x)$.

$-5=-\frac{2}{3}x+3$

Subtract $3$ from both sides.

$-8=-\frac{2}{3}x$

Get the $x$-term alone.

$\left(-\frac{3}{2}\right)(-8)=\left(-\frac{2}{3}x\right)\left(-\frac{3}{2}\right)$

$x=12$

Substitute $−3$ for each $x$ in $g(x)$.

$g(−3)=2(−3)^2−5$

Simplify.

Substitute $−7$ for $g(x)$.

$−7=2x^2−5$

Solve.

$x^2=−1$

No solution.

Substitute $8$ for $g(x)$.

$8=2x^2−5$

Solve.

$x^2=\frac{13}{2}$

$x=\pm\sqrt\frac{13}{2}$

Substitute $9$ for $g(x)$.

$9=2x^2−5$

Solve.

$x^2=7$

Remember, there should be 2 solutions.