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Solve using the quadratic formula.\newline9y2−3y−7=09y^2 - 3y - 7 = 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.\newline9y2−3y−7=09y^2 - 3y - 7 = 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. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 9y2−3y−7=09y^2 − 3y − 7 = 0. The quadratic equation is in the form ay2+by+c=0ay^2 + by + c = 0. Comparing this with our equation, we get: a=9a = 9 b=−3b = -3 c=−7c = -7
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula y=−b±b2−4ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=9a = 9, b=−3b = -3, and c=−7c = -7 into the formula. y=−(−3)±(−3)2−4⋅9⋅(−7)2⋅9y = \frac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot9\cdot(-7)}}{2\cdot9} y=3±9+25218y = \frac{3 \pm \sqrt{9 + 252}}{18}
  3. Simplify and calculate: Simplify the expression under the square root and calculate the discriminant. 9+252\sqrt{9 + 252} = 261\sqrt{261}
  4. Continue with formula: Continue with the quadratic formula using the simplified discriminant.\newliney=3±26118y = \frac{3 \pm \sqrt{261}}{18}\newlineNow we have two possible solutions for yy:\newliney=3+26118y = \frac{3 + \sqrt{261}}{18} or y=3−26118y = \frac{3 - \sqrt{261}}{18}
  5. Calculate numerical values: Calculate the numerical values of yy and round to the nearest hundredth if necessary.\newlineFirst solution:\newliney=3+26118y = \frac{3 + \sqrt{261}}{18}\newliney≈3+16.1618y \approx \frac{3 + 16.16}{18}\newliney≈19.1618y \approx \frac{19.16}{18}\newliney≈1.06y \approx 1.06\newlineSecond solution:\newliney=3−26118y = \frac{3 - \sqrt{261}}{18}\newliney≈3−16.1618y \approx \frac{3 - 16.16}{18}\newliney≈−13.1618y \approx \frac{-13.16}{18}\newliney≈−0.73y \approx -0.73

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