Final answer:
To solve the quadratic 6t^2 + 1 = 3t, convert it to 6t^2 - 3t + 1 = 0 and use the quadratic formula. With a = 6, b = -3, and c = 1, we find the discriminant is negative, indicating no real solutions, only complex ones.
Step-by-step explanation:
To solve the quadratic equation 6t^2 + 1 = 3t using the quadratic formula, we first need to rearrange the equation into standard form, which is at^2 + bt + c = 0. In this case, we subtract 3t from both sides to get 6t^2 - 3t + 1 = 0. Now the equation is in the correct format, with a = 6, b = -3, and c = 1.
Next, we apply the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Substituting our values we get:
t = (3 ± √((-3)^2 - 4(6)(1))) / (2*6)
t = (3 ± √(9 - 24)) / 12
t = (3 ± √(-15)) / 12
Since the discriminant (b^2 - 4ac) is negative, this equation has no real solutions. It only has complex solutions because the square root of a negative number is imaginary.