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Solve using the quadratic formula.\newline3h2+8h−9=03h^2 + 8h - 9 = 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.\newline3h2+8h−9=03h^2 + 8h - 9 = 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 of the quadratic equation.\newlineThe quadratic equation is in the form ah2+bh+c=0a h^2 + b h + c = 0. For the equation 3h2+8h−9=03 h^2 + 8 h - 9 = 0, the coefficients are:\newlinea=3a = 3\newlineb=8b = 8\newlinec=−9c = -9
  2. Substitute into formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is h=−b±b2−4ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values of aa, bb, and cc, we get:\newlineh=−(8)±(8)2−4⋅3⋅(−9)2⋅3h = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot3\cdot(-9)}}{2\cdot3}
  3. Simplify discriminant: Simplify the expression under the square root.\newlineCalculate the discriminant b2−4acb^2 - 4ac:\newlineDiscriminant = (8)2−4⋅3⋅(−9)(8)^2 - 4\cdot 3\cdot (-9)\newlineDiscriminant = 64+10864 + 108\newlineDiscriminant = 172172
  4. Continue with formula: Continue with the quadratic formula.\newlineNow we have the discriminant, we can continue with the formula:\newlineh=−8±1726h = \frac{{-8 \pm \sqrt{172}}}{{6}}
  5. Simplify square root: Simplify the square root, if possible.\newlineThe square root of 172172 cannot be simplified to an integer, so we leave it as 172\sqrt{172}.
  6. Calculate possible solutions: Calculate the two possible solutions for hh.h=−8+1726h = \frac{{-8 + \sqrt{172}}}{{6}} or h=−8−1726h = \frac{{-8 - \sqrt{172}}}{{6}}
  7. Round to nearest hundredth: Round the values of hh to the nearest hundredth, if required.h≈(−8+13.11)/6h \approx (-8 + 13.11) / 6 or h≈(−8−13.11)/6h \approx (-8 - 13.11) / 6h≈5.11/6h \approx 5.11 / 6 or h≈−21.11/6h \approx -21.11 / 6h≈0.85h \approx 0.85 or h≈−3.52h \approx -3.52

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