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Solve using the quadratic formula.\newline6h2−9h+3=06h^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.\newline6h2−9h+3=06h^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 values: Identify the values of aa, bb, and cc in the quadratic equation 6h2−9h+3=06h^2 − 9h + 3 = 0. The quadratic equation is in the form ah2+bh+c=0ah^2 + bh + c = 0, so by comparison: a=6a = 6 b=−9b = -9 c=3c = 3
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find hh. The quadratic formula is h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: h=−(−9)±(−9)2−4⋅6⋅32⋅6h = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot6\cdot3}}{2\cdot6}
  3. Calculate discriminant: Simplify the terms inside the square root and calculate the discriminant b2−4acb^2 - 4ac.(−9)2−4⋅6⋅3=81−72=9\sqrt{(-9)^2 - 4\cdot 6\cdot 3} = \sqrt{81 - 72} = \sqrt{9}
  4. Simplify formula: Continue simplifying the quadratic formula with the calculated discriminant.\newlineh=9±912h = \frac{9 \pm \sqrt{9}}{12}\newlineh=9±312h = \frac{9 \pm 3}{12}
  5. Find possible values: Find the two possible values for hh.h=(9+3)12h = \frac{(9 + 3)}{12} or h=(9−3)12h = \frac{(9 - 3)}{12}h=1212h = \frac{12}{12} or h=612h = \frac{6}{12}h=1h = 1 or h=12h = \frac{1}{2}
  6. Write final answers: Simplify the fractions and write the final answers.\newlineh=1h = 1 or h=12h = \frac{1}{2}\newlineSince 12\frac{1}{2} is already in simplest form, we do not need to round to the nearest hundredth.

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