3t^2+6t-13=0

Solution for 3t^2+6t-13=0 equation:

Simplifying
3t2 + 6t + -13 = 0

Reorder the terms:
-13 + 6t + 3t2 = 0

Solving
-13 + 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'.
-4.333333333 + 2t + t2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 2t + 4.333333333 + t2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 2t + t2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 2t + t2 = 0 + 4.333333333
2t + t2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
2t + t2 = 4.333333333

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 = 4.333333333 + 1

Reorder the terms:
1 + 2t + t2 = 4.333333333 + 1

Combine like terms: 4.333333333 + 1 = 5.333333333
1 + 2t + t2 = 5.333333333

Factor a perfect square on the left side:
(t + 1)(t + 1) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(t + 1) equal to 2.309401077 and -2.309401077.

Subproblem 1
t + 1 = 2.309401077

Simplifying
t + 1 = 2.309401077

Reorder the terms:
1 + t = 2.309401077

Solving
1 + t = 2.309401077

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 = 2.309401077 + -1

Combine like terms: 1 + -1 = 0
0 + t = 2.309401077 + -1
t = 2.309401077 + -1

Combine like terms: 2.309401077 + -1 = 1.309401077
t = 1.309401077

Simplifying
t = 1.309401077

Subproblem 2
t + 1 = -2.309401077

Simplifying
t + 1 = -2.309401077

Reorder the terms:
1 + t = -2.309401077

Solving
1 + t = -2.309401077

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 = -2.309401077 + -1

Combine like terms: 1 + -1 = 0
0 + t = -2.309401077 + -1
t = -2.309401077 + -1

Combine like terms: -2.309401077 + -1 = -3.309401077
t = -3.309401077

Simplifying
t = -3.309401077

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.309401077, -3.309401077}