6t^2+6t-11=0

Solution for 6t^2+6t-11=0 equation:

Simplifying
6t2 + 6t + -11 = 0

Reorder the terms:
-11 + 6t + 6t2 = 0

Solving
-11 + 6t + 6t2 = 0

Solving for variable 't'.

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

Divide each side by '6'.
-1.833333333 + t + t2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + t + 1.833333333 + t2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + t + t2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + t + t2 = 0 + 1.833333333
t + t2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
t + t2 = 1.833333333

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + t2 = 1.833333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 1.833333333 + 0.25

Combine like terms: 1.833333333 + 0.25 = 2.083333333
1.25 + t2 = 2.083333333

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2.083333333

Calculate the square root of the right side: 1.443375673

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.443375673 and -1.443375673.

Subproblem 1
t + 0.5 = 1.443375673

Simplifying
t + 0.5 = 1.443375673

Reorder the terms:
0.5 + t = 1.443375673

Solving
0.5 + t = 1.443375673

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 1.443375673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 1.443375673 + -0.5
t = 1.443375673 + -0.5

Combine like terms: 1.443375673 + -0.5 = 0.943375673
t = 0.943375673

Simplifying
t = 0.943375673

Subproblem 2
t + 0.5 = -1.443375673

Simplifying
t + 0.5 = -1.443375673

Reorder the terms:
0.5 + t = -1.443375673

Solving
0.5 + t = -1.443375673

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -1.443375673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -1.443375673 + -0.5
t = -1.443375673 + -0.5

Combine like terms: -1.443375673 + -0.5 = -1.943375673
t = -1.943375673

Simplifying
t = -1.943375673

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.943375673, -1.943375673}