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Solve using the quadratic formula.\newline3z2−4z−7=03z^2 - 4z - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____

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Q. Solve using the quadratic formula.\newline3z2−4z−7=03z^2 - 4z - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation 3z2−4z−7=03z^2 - 4z - 7 = 0. Here, a=3a = 3, b=−4b = -4, and c=−7c = -7.
  2. Recall quadratic formula: Recall the quadratic formula, which is z=−b±b2−4ac2az = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. \newline
  4. Simplify equation: Simplify the square root and the equation.\newlinez=4±106z = \frac{4 \pm 10}{6}\newlineThis gives us two possible solutions for zz.
  5. Calculate first solution: Calculate the first solution by adding the square root result.\newlinez=(4+10)/6z = (4 + 10) / 6\newlinez=14/6z = 14 / 6\newlinez=7/3z = 7 / 3
  6. Calculate second solution: Calculate the second solution by subtracting the square root result.\newlinez=(4−10)/6z = (4 - 10) / 6\newlinez=−6/6z = -6 / 6\newlinez=−1z = -1

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