(3t^2)+6t-101=0

Solution for (3t^2)+6t-101=0 equation:

Simplifying
(3t2) + 6t + -101 = 0

Reorder the terms:
-101 + 6t + (3t2) = 0

Solving
-101 + 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'.
-33.66666667 + 2t + t2 = 0

Move the constant term to the right:

Add '33.66666667' to each side of the equation.
-33.66666667 + 2t + 33.66666667 + t2 = 0 + 33.66666667

Reorder the terms:
-33.66666667 + 33.66666667 + 2t + t2 = 0 + 33.66666667

Combine like terms: -33.66666667 + 33.66666667 = 0.00000000
0.00000000 + 2t + t2 = 0 + 33.66666667
2t + t2 = 0 + 33.66666667

Combine like terms: 0 + 33.66666667 = 33.66666667
2t + t2 = 33.66666667

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 = 33.66666667 + 1

Reorder the terms:
1 + 2t + t2 = 33.66666667 + 1

Combine like terms: 33.66666667 + 1 = 34.66666667
1 + 2t + t2 = 34.66666667

Factor a perfect square on the left side:
((t) + 1)((t) + 1) = 34.66666667

Calculate the square root of the right side: 5.887840578

Break this problem into two subproblems by setting 
((t) + 1) equal to 5.887840578 and -5.887840578.

Subproblem 1
(t) + 1 = 5.887840578

Simplifying
(t) + 1 = 5.887840578
t + 1 = 5.887840578

Reorder the terms:
1 + t = 5.887840578

Solving
1 + t = 5.887840578

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 = 5.887840578 + -1

Combine like terms: 1 + -1 = 0
0 + t = 5.887840578 + -1
t = 5.887840578 + -1

Combine like terms: 5.887840578 + -1 = 4.887840578
t = 4.887840578

Simplifying
t = 4.887840578

Subproblem 2
(t) + 1 = -5.887840578

Simplifying
(t) + 1 = -5.887840578
t + 1 = -5.887840578

Reorder the terms:
1 + t = -5.887840578

Solving
1 + t = -5.887840578

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 = -5.887840578 + -1

Combine like terms: 1 + -1 = 0
0 + t = -5.887840578 + -1
t = -5.887840578 + -1

Combine like terms: -5.887840578 + -1 = -6.887840578
t = -6.887840578

Simplifying
t = -6.887840578

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.887840578, -6.887840578}