3-8t+3t^2=0

Solution for 3-8t+3t^2=0 equation:

Simplifying
3 + -8t + 3t2 = 0

Solving
3 + -8t + 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'.
1 + -2.666666667t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.666666667t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -2.666666667t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.666666667t + t2 = 0 + -1
-2.666666667t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.666666667t + t2 = -1

The t term is -2.666666667t.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667t + 1.777777780 + t2 = -1 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667t + t2 = -1 + 1.777777780

Combine like terms: -1 + 1.777777780 = 0.77777778
1.777777780 + -2.666666667t + t2 = 0.77777778

Factor a perfect square on the left side:
(t + -1.333333334)(t + -1.333333334) = 0.77777778

Calculate the square root of the right side: 0.881917105

Break this problem into two subproblems by setting 
(t + -1.333333334) equal to 0.881917105 and -0.881917105.

Subproblem 1
t + -1.333333334 = 0.881917105

Simplifying
t + -1.333333334 = 0.881917105

Reorder the terms:
-1.333333334 + t = 0.881917105

Solving
-1.333333334 + t = 0.881917105

Solving for variable 't'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + t = 0.881917105 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + t = 0.881917105 + 1.333333334
t = 0.881917105 + 1.333333334

Combine like terms: 0.881917105 + 1.333333334 = 2.215250439
t = 2.215250439

Simplifying
t = 2.215250439

Subproblem 2
t + -1.333333334 = -0.881917105

Simplifying
t + -1.333333334 = -0.881917105

Reorder the terms:
-1.333333334 + t = -0.881917105

Solving
-1.333333334 + t = -0.881917105

Solving for variable 't'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + t = -0.881917105 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + t = -0.881917105 + 1.333333334
t = -0.881917105 + 1.333333334

Combine like terms: -0.881917105 + 1.333333334 = 0.451416229
t = 0.451416229

Simplifying
t = 0.451416229

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.215250439, 0.451416229}