1. **State the problem:** We need to evaluate the expression $b^2 - ac$ given the values $a = -2 \times \frac{1}{2}$, $b = -0.8$, and $c = \frac{1}{5}$.\n\n2. **Calculate $a$:** Multiply $-2$ by $\frac{1}{2}$:\n$$a = -2 \times \frac{1}{2} = -1$$\n\n3. **Recall the formula:** The expression is $b^2 - ac$. This means square $b$ and subtract the product of $a$ and $c$.\n\n4. **Calculate $b^2$:**\n$$b^2 = (-0.8)^2 = 0.64$$\n\n5. **Calculate $ac$:**\n$$ac = (-1) \times \frac{1}{5} = -\frac{1}{5} = -0.2$$\n\n6. **Evaluate $b^2 - ac$:**\n$$b^2 - ac = 0.64 - (-0.2) = 0.64 + 0.2 = 0.84$$\n\n**Final answer:** $b^2 - ac = 0.84$