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Solve using the quadratic formula.\newline3y2−6y−4=03y^2 - 6y - 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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Q. Solve using the quadratic formula.\newline3y2−6y−4=03y^2 - 6y - 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 3y2−6y−4=03y^2 − 6y − 4 = 0. The quadratic equation is in the form ay2+by+c=0ay^2 + by + c = 0. For our equation, a=3a = 3, b=−6b = -6, and bb00.
  2. Substitute values into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula y=−b±b2−4ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. The quadratic formula is y=−(−6)±(−6)2−4⋅3⋅(−4)2⋅3y = \frac{-(-6) \pm \sqrt{(-6)^2 - 4\cdot3\cdot(-4)}}{2\cdot3}.
  3. Simplify expression inside square root: Simplify the expression inside the square root and the constants outside the square root.\newlineCalculate (−6)2(-6)^2, which is 3636, and 4×3×(−4)4 \times 3 \times (-4), which is −48-48. The expression inside the square root becomes 36−(−48)\sqrt{36 - (-48)}.
  4. Further simplify inside square root: Further simplify the expression inside the square root. 36−(−48)\sqrt{36 - (-48)} simplifies to 36+48\sqrt{36 + 48} which is 84\sqrt{84}.
  5. Simplify 84\sqrt{84}: Simplify 84\sqrt{84} to its simplest radical form.84\sqrt{84} can be simplified to 4×21\sqrt{4\times21} which is 2×212\times\sqrt{21}.
  6. Substitute simplified square root: Substitute the simplified square root back into the quadratic formula.\newlineThe quadratic formula now becomes y=6±2216y = \frac{6 \pm 2\sqrt{21}}{6}.
  7. Simplify quadratic formula: Simplify the quadratic formula by dividing all terms by the common factor of 66. y=(1±(13)21)y = (1 \pm (\frac{1}{3})\sqrt{21}). This gives us two possible solutions for yy.
  8. Calculate two possible solutions: Calculate the two possible solutions for yy. The first solution is y=1+1321y = 1 + \frac{1}{3}\sqrt{21}, and the second solution is y=1−1321y = 1 - \frac{1}{3}\sqrt{21}.
  9. Round values of y: If necessary, round the values of yy to the nearest hundredth.y≈1+0.333×4.58y \approx 1 + 0.333 \times 4.58 or y≈1−0.333×4.58y \approx 1 - 0.333 \times 4.58y≈1+1.53y \approx 1 + 1.53 or y≈1−1.53y \approx 1 - 1.53y≈2.53y \approx 2.53 or y≈−0.53y \approx -0.53

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