$$ Three\ test\ scores=78,86,82 $$

$$ Three\ scores\ weighted=20\%=0.2 $$

$$ Final\ scores\ weighted=40\%=0.4 $$

$$ Final\ scores=x=? $$

So we have,

$$ 78(0.2)+86(0.2)+85(0.2)+0.4x\geq 86 $$

$$ 246(0.2)+0.4x\geq 86 $$

$$ 246(0.2)+0.4x\geq 86 $$

$$ 49.2+0.4x\geq 86 $$

$$ x\geq \frac{36.8}{0.4} $$

$$ \therefore x\geq 92 $$