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Solve using the quadratic formula.\newline5t2+8t−6=05t^2 + 8t - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____

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Q. Solve using the quadratic formula.\newline5t2+8t−6=05t^2 + 8t - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____
  1. Identify Coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form at2+bt+c=0at^2 + bt + c = 0. For the equation 5t2+8t−6=05t^2 + 8t - 6 = 0, the coefficients are:\newlinea = 55\newlineb = 88\newlinec = −6-6
  2. Substitute into Formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is t=−b±b2−4ac2at = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get:\newlinet=−(8)±(8)2−4(5)(−6)2(5)t = \frac{-(8) \pm \sqrt{(8)^2 - 4(5)(-6)}}{2(5)}
  3. Simplify Equation: Simplify under the square root and the denominator.\newlinet=−8±64+12010t = \frac{-8 \pm \sqrt{64 + 120}}{10}\newlinet=−8±18410t = \frac{-8 \pm \sqrt{184}}{10}
  4. Calculate Solutions: Simplify the square root (if possible) and calculate the solutions.\newlineSince 184184 is not a perfect square, we will leave it under the square root. We have two possible solutions:\newlinet=−8+18410t = \frac{-8 + \sqrt{184}}{10} or t=−8−18410t = \frac{-8 - \sqrt{184}}{10}
  5. Round to Nearest Hundredth: Simplify the solutions further if possible and round to the nearest hundredth if necessary.\newlinet=−8+18410≈−8+13.5610t = \frac{-8 + \sqrt{184}}{10} \approx \frac{-8 + 13.56}{10} or t=−8−18410≈−8−13.5610t = \frac{-8 - \sqrt{184}}{10} \approx \frac{-8 - 13.56}{10}\newlinet≈5.5610t \approx \frac{5.56}{10} or t≈−21.5610t \approx \frac{-21.56}{10}\newlinet≈0.56t \approx 0.56 or t≈−2.16t \approx -2.16

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