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Solve using the quadratic formula.\newline4h2+3h−5=04h^2 + 3h - 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.\newline4h2+3h−5=04h^2 + 3h - 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 values: Identify the values of aa, bb, and cc in the quadratic equation 4h2+3h−5=04h^2 + 3h - 5 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=4a = 4 b=3b = 3 c=−5c = -5
  2. Substitute values: 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=−(3)±(3)2−4⋅4⋅(−5)2⋅4h = \frac{-(3) \pm \sqrt{(3)^2 - 4\cdot4\cdot(-5)}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (3)2−4⋅4⋅(−5)=9+80=89\sqrt{(3)^2 - 4\cdot4\cdot(-5)} = \sqrt{9 + 80} = \sqrt{89}
  4. Continue with formula: Continue with the quadratic formula using the simplified discriminant. \newlineh=−3±898h = \frac{-3 \pm \sqrt{89}}{8}\newlineThis gives us two possible solutions for hh.
  5. Calculate possible values: Calculate the two possible values for hh.\newlineFirst solution:\newlineh=−3+898h = \frac{-3 + \sqrt{89}}{8}\newlineSecond solution:\newlineh=−3−898h = \frac{-3 - \sqrt{89}}{8}
  6. Round to nearest hundredth: Round the values of hh to the nearest hundredth, if necessary.\newlineFirst solution:\newlineh≈(−3+9.43)/8h \approx (-3 + 9.43) / 8\newlineh≈6.43/8h \approx 6.43 / 8\newlineh≈0.80h \approx 0.80\newlineSecond solution:\newlineh≈(−3−9.43)/8h \approx (-3 - 9.43) / 8\newlineh≈−12.43/8h \approx -12.43 / 8\newlineh≈−1.55h \approx -1.55

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