1. **State the problem:** Solve the quadratic equation $$\frac{3}{5}y^2 + \frac{2}{5}y = \frac{16}{5}$$ for $y$. 2. **Rewrite the equation:** Multiply both sides by 5 to clear denominators: $$3y^2 + 2y = 16$$ 3. **Bring all terms to one side:** $$3y^2 + 2y - 16 = 0$$ 4. **Identify coefficients:** $$a = 3, \quad b = 2, \quad c = -16$$ 5. **Use the quadratic formula:** $$y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 6. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 2^2 - 4 \times 3 \times (-16) = 4 + 192 = 196$$ 7. **Find the square root of the discriminant:** $$\sqrt{196} = 14$$ 8. **Substitute values into the formula:** $$y = \frac{-2 \pm 14}{2 \times 3} = \frac{-2 \pm 14}{6}$$ 9. **Calculate the two solutions:** - For the plus sign: $$y = \frac{-2 + 14}{6} = \frac{12}{6} = 2$$ - For the minus sign: $$y = \frac{-2 - 14}{6} = \frac{-16}{6} = -\frac{8}{3}$$ **Final answer:** $$y = 2, -\frac{8}{3}$$