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Solve using the quadratic formula.\newline2h2+9h+3=02h^2 + 9h + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____

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Q. Solve using the quadratic formula.\newline2h2+9h+3=02h^2 + 9h + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 2h2+9h+3=02h^2 + 9h + 3 = 0.a=2a = 2, b=9b = 9, c=3c = 3
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula: h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineh=−(9)±(9)2−4⋅2⋅32⋅2h = \frac{-(9) \pm \sqrt{(9)^2 - 4\cdot2\cdot3}}{2\cdot2}
  3. Calculate discriminant: Calculate the discriminant: b2−4acb^2 - 4ac.\newlineDiscriminant = (9)2−4⋅2⋅3=81−24=57(9)^2 - 4\cdot 2\cdot 3 = 81 - 24 = 57
  4. Insert into formula and simplify: Insert the discriminant into the quadratic formula and simplify.\newlineh=−9±574h = \frac{-9 \pm \sqrt{57}}{4}
  5. Identify possible values for h: Identify the two possible values for hh.h=−9+574h = \frac{{-9 + \sqrt{57}}}{{4}} or h=−9−574h = \frac{{-9 - \sqrt{57}}}{{4}}
  6. Round values to nearest hundredth: Round the values of hh to the nearest hundredth, if necessary.h≈(−9+7.55)/4h \approx (-9 + 7.55) / 4 or h≈(−9−7.55)/4h \approx (-9 - 7.55) / 4h≈−1.45/4h \approx -1.45 / 4 or h≈−16.55/4h \approx -16.55 / 4h≈−0.36h \approx -0.36 or h≈−4.14h \approx -4.14

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