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Solve using the quadratic formula.\newline2y2+9y+3=02y^2 + 9y + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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Q. Solve using the quadratic formula.\newline2y2+9y+3=02y^2 + 9y + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Quadratic Formula Explanation: The quadratic formula is given by y=−b±b2−4ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms in the quadratic equation ay2+by+c=0ay^2 + by + c = 0. In this case, a=2a = 2, b=9b = 9, and c=3c = 3.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is 92−4(2)(3)9^2 - 4(2)(3).
  3. Find Discriminant Value: Perform the calculation: 81−24=5781 - 24 = 57. This is the value of the discriminant.
  4. Plug Values into Formula: Now, plug the values of aa, bb, and the discriminant into the quadratic formula to find the two possible values for yy.y=−9±574.y = \frac{-9 \pm \sqrt{57}}{4}.
  5. Calculate Positive Solution: Calculate the two possible solutions for yy. First, the positive square root:\newliney=−9+574y = \frac{{-9 + \sqrt{57}}}{{4}}.
  6. Positive Solution Calculation: Perform the calculation for the first solution:\newliney≈(−9+7.55)/4y \approx (-9 + 7.55) / 4\newliney≈−1.45/4y \approx -1.45 / 4\newliney≈−0.3625y \approx -0.3625, rounded to the nearest hundredth, y≈−0.36y \approx -0.36.
  7. Calculate Negative Solution: Now, calculate the second solution using the negative square root: y=−9−574y = \frac{{-9 - \sqrt{57}}}{{4}}.
  8. Negative Solution Calculation: Perform the calculation for the second solution:\newliney≈(−9−7.55)/4y \approx (-9 - 7.55) / 4\newliney≈−16.55/4y \approx -16.55 / 4\newliney≈−4.1375y \approx -4.1375, rounded to the nearest hundredth, y≈−4.14y \approx -4.14.

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