3t^2-9t+2=0

Solution for 3t^2-9t+2=0 equation:

Simplifying
3t2 + -9t + 2 = 0

Reorder the terms:
2 + -9t + 3t2 = 0

Solving
2 + -9t + 3t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.6666666667 + -3t + t2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3t + -0.6666666667 + t2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3t + t2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3t + t2 = 0 + -0.6666666667
-3t + t2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3t + t2 = -0.6666666667

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -0.6666666667 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -0.6666666667 + 2.25

Combine like terms: -0.6666666667 + 2.25 = 1.5833333333
2.25 + -3t + t2 = 1.5833333333

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 1.5833333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.258305739 and -1.258305739.

Subproblem 1
t + -1.5 = 1.258305739

Simplifying
t + -1.5 = 1.258305739

Reorder the terms:
-1.5 + t = 1.258305739

Solving
-1.5 + t = 1.258305739

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.258305739 + 1.5
t = 1.258305739 + 1.5

Combine like terms: 1.258305739 + 1.5 = 2.758305739
t = 2.758305739

Simplifying
t = 2.758305739

Subproblem 2
t + -1.5 = -1.258305739

Simplifying
t + -1.5 = -1.258305739

Reorder the terms:
-1.5 + t = -1.258305739

Solving
-1.5 + t = -1.258305739

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.258305739 + 1.5
t = -1.258305739 + 1.5

Combine like terms: -1.258305739 + 1.5 = 0.241694261
t = 0.241694261

Simplifying
t = 0.241694261

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.758305739, 0.241694261}