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Your input: solve the quadratic equation $$$3 r^{2} + 8 r + 5 = 0$$$ by using quadratic formula.

The standard quadratic equation has the form $$$ar^2+br+c=0$$$.

In our case, $$$a=3$$$, $$$b=8$$$, $$$c=5$$$.

Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=8^2-4\cdot 3 \cdot 5=4$$$.

Find the roots of the equation using the formulas $$$r_1=\frac{-b-\sqrt{D}}{2a}$$$ and $$$r_2=\frac{-b+\sqrt{D}}{2a}$$$

$$$r_1=\frac{-8-\sqrt{4}}{2\cdot 3}=- \frac{5}{3}$$$ and $$$r_2=\frac{-8+\sqrt{4}}{2\cdot 3}=-1$$$

Answer: $$$r_1=- \frac{5}{3}$$$; $$$r_2=-1$$$