Final answer:
To solve the equation 10t² + 21t + 6 = 2t using the quadratic formula, rearrange the equation to get it in the form ax² + bx + c = 0. Substitute the values of a, b, and c into the quadratic formula and simplify to find the solutions for t.
Step-by-step explanation:
To solve the equation 10t² + 21t + 6 = 2t using the quadratic formula, we need to rearrange the equation to get it in the form ax² + bx + c = 0. In this case, the equation becomes 10t² + 19t + 6 = 0. Now, we can identify the values for a, b, and c, which are 10, 19, and 6 respectively.
Using the quadratic formula, t = (-b ± √(b² - 4ac)) / (2a), we can substitute the values into the formula: t = (-19 ± √(19² - 4(10)(6))) / (2(10)).
Simplifying the equation further, we have t = (-19 ± √(361 - 240)) / (20), which becomes t = (-19 ± √(121)) / (20).
Finally, we can find two solutions for t: t = (-19 + 11) / 20 and t = (-19 - 11) / 20. Solving these equations gives us t = -4/5 and t = -3/2.