Answer:
t = 1/3 + (i sqrt(53))/3 or t = 1/3 - (i sqrt(53))/3
Explanation:
Solve for t:
3 t^2 = 2 (t - 9)
Expand out terms of the right hand side:
3 t^2 = 2 t - 18
Subtract 2 t - 18 from both sides:
3 t^2 - 2 t + 18 = 0
Divide both sides by 3:
t^2 - (2 t)/3 + 6 = 0
Subtract 6 from both sides:
t^2 - (2 t)/3 = -6
Add 1/9 to both sides:
t^2 - (2 t)/3 + 1/9 = -53/9
Write the left hand side as a square:
(t - 1/3)^2 = -53/9
Take the square root of both sides:
t - 1/3 = (i sqrt(53))/3 or t - 1/3 = -(i sqrt(53))/3
Add 1/3 to both sides:
t = 1/3 + (i sqrt(53))/3 or t - 1/3 = -(i sqrt(53))/3
Add 1/3 to both sides:
Answer: t = 1/3 + (i sqrt(53))/3 or t = 1/3 - (i sqrt(53))/3