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Solve using the quadratic formula.\newline6h2−9h−5=06h^2 - 9h - 5 = 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−5=06h^2 - 9h - 5 = 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 6h2−9h−5=06h^2 − 9h − 5 = 0. The quadratic equation is in the form ah2+bh+c=0ah^2 + bh + c = 0. For our equation, a=6a = 6, b=−9b = -9, and c=−5c = -5.
  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}. The quadratic formula is h=−(−9)±(−9)2−4⋅6⋅(−5)2⋅6h = \frac{-(-9) \pm \sqrt{(-9)^2 - 4 \cdot 6 \cdot (-5)}}{2 \cdot 6}.
  3. Simplify expression inside square root: Simplify the expression inside the square root b2−4ac\sqrt{b^2 - 4ac}.\newlineCalculate (−9)2−4⋅6⋅(−5)=81+120=201\sqrt{(-9)^2 - 4\cdot 6\cdot (-5)} = \sqrt{81 + 120} = \sqrt{201}.
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the values obtained. h=9±20112h = \frac{9 \pm \sqrt{201}}{12}.
  5. Calculate two possible solutions: Calculate the two possible solutions for hh.
    First solution: h=9+20112h = \frac{9 + \sqrt{201}}{12}.
    Second solution: h=9−20112h = \frac{9 - \sqrt{201}}{12}.
  6. Round values to nearest hundredth: Round the values of hh to the nearest hundredth, if necessary.\newlineFirst solution: h≈(9+14.18)/12≈23.18/12≈1.93h \approx (9 + 14.18) / 12 \approx 23.18 / 12 \approx 1.93.\newlineSecond solution: h≈(9−14.18)/12≈−5.18/12≈−0.43h \approx (9 - 14.18) / 12 \approx -5.18 / 12 \approx -0.43.

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