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Solve using the quadratic formula.\newline6n2+9n−6=06n^2 + 9n - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinen=n = _____ or n=n = _____

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Q. Solve using the quadratic formula.\newline6n2+9n−6=06n^2 + 9n - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinen=n = _____ or n=n = _____
  1. Identify values of aa, bb, and cc: Identify values of aa, bb, and cc from the equation 6n2+9n−6=06n^2 + 9n - 6 = 0.\newlinea=6a = 6, b=9b = 9, c=−6c = -6.
  2. Plug into quadratic formula: Plug aa, bb, and cc into the quadratic formula: n=−b±b2−4ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlinen=−(9)±(9)2−4(6)(−6)2(6)n = \frac{-(9) \pm \sqrt{(9)^2 - 4(6)(-6)}}{2(6)}.
  3. Simplify square root: Simplify inside the square root: 81+144\sqrt{81 + 144}.225\sqrt{225}.
  4. Calculate possible solutions: Square root of 225225 is 1515.n=−9±1512n = \frac{{-9 \pm 15}}{{12}}.
  5. Simplify fractions: Calculate the two possible solutions for nn.n=−9+1512n = \frac{{-9 + 15}}{{12}} or n=−9−1512n = \frac{{-9 - 15}}{{12}}.n=612n = \frac{{6}}{{12}} or n=−2412n = \frac{{-24}}{{12}}.
  6. Simplify fractions: Calculate the two possible solutions for nn.n=−9+1512n = \frac{-9 + 15}{12} or n=−9−1512n = \frac{-9 - 15}{12}.n=612n = \frac{6}{12} or n=−2412n = \frac{-24}{12}.Simplify both fractions.n=12n = \frac{1}{2} or n=−2n = -2.

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