3t^2+6t-4=0

Solution for 3t^2+6t-4=0 equation:

Simplifying
3t2 + 6t + -4 = 0

Reorder the terms:
-4 + 6t + 3t2 = 0

Solving
-4 + 6t + 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'.
-1.333333333 + 2t + t2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 2t + 1.333333333 + t2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 2t + t2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 2t + t2 = 0 + 1.333333333
2t + t2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
2t + t2 = 1.333333333

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 1.333333333 + 1

Reorder the terms:
1 + 2t + t2 = 1.333333333 + 1

Combine like terms: 1.333333333 + 1 = 2.333333333
1 + 2t + t2 = 2.333333333

Factor a perfect square on the left side:
(t + 1)(t + 1) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(t + 1) equal to 1.527525232 and -1.527525232.

Subproblem 1
t + 1 = 1.527525232

Simplifying
t + 1 = 1.527525232

Reorder the terms:
1 + t = 1.527525232

Solving
1 + t = 1.527525232

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 1.527525232 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.527525232 + -1
t = 1.527525232 + -1

Combine like terms: 1.527525232 + -1 = 0.527525232
t = 0.527525232

Simplifying
t = 0.527525232

Subproblem 2
t + 1 = -1.527525232

Simplifying
t + 1 = -1.527525232

Reorder the terms:
1 + t = -1.527525232

Solving
1 + t = -1.527525232

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -1.527525232 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.527525232 + -1
t = -1.527525232 + -1

Combine like terms: -1.527525232 + -1 = -2.527525232
t = -2.527525232

Simplifying
t = -2.527525232

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.527525232, -2.527525232}