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 = 2.9166666667
2.25 + 3t + t2 = 2.9166666667

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 2.9166666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(t + 1.5) equal to 1.707825128 and -1.707825128.

Subproblem 1
t + 1.5 = 1.707825128

Simplifying
t + 1.5 = 1.707825128

Reorder the terms:
1.5 + t = 1.707825128

Solving
1.5 + t = 1.707825128

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 = 1.707825128 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 1.707825128 + -1.5
t = 1.707825128 + -1.5

Combine like terms: 1.707825128 + -1.5 = 0.207825128
t = 0.207825128

Simplifying
t = 0.207825128

Subproblem 2
t + 1.5 = -1.707825128

Simplifying
t + 1.5 = -1.707825128

Reorder the terms:
1.5 + t = -1.707825128

Solving
1.5 + t = -1.707825128

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 = -1.707825128 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -1.707825128 + -1.5
t = -1.707825128 + -1.5

Combine like terms: -1.707825128 + -1.5 = -3.207825128
t = -3.207825128

Simplifying
t = -3.207825128

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.207825128, -3.207825128}