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Solve using the quadratic formula.\newline2y2+7y+6=02y^2 + 7y + 6 = 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+7y+6=02y^2 + 7y + 6 = 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 Definition: 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 quadratic equation ay2+by+c=0ay^2 + by + c = 0. In this case, a=2a = 2, b=7b = 7, and c=6c = 6.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is 72−4(2)(6)7^2 - 4(2)(6).
  3. Discriminant Calculation: Perform the calculation: 72−4(2)(6)=49−48=17^2 - 4(2)(6) = 49 - 48 = 1.
  4. Using Quadratic Formula: Now that we have the discriminant, we can use the quadratic formula. Since the discriminant is positive, we will have two real solutions. Substitute aa, bb, and the discriminant into the formula to find yy.
  5. First Solution Calculation: First solution: y=−7+12×2=−7+14=−64=−32y = \frac{-7 + \sqrt{1}}{2 \times 2} = \frac{-7 + 1}{4} = \frac{-6}{4} = -\frac{3}{2}.
  6. Second Solution Calculation: Second solution: y=−7−12×2=−7−14=−84=−2y = \frac{-7 - \sqrt{1}}{2 \times 2} = \frac{-7 - 1}{4} = \frac{-8}{4} = -2.

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