3t^2+15t+2=0

Solution for 3t^2+15t+2=0 equation:

Simplifying
3t2 + 15t + 2 = 0

Reorder the terms:
2 + 15t + 3t2 = 0

Solving
2 + 15t + 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 + 5t + t2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 5t + -0.6666666667 + t2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 5t + t2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 5t + t2 = 0 + -0.6666666667
5t + t2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
5t + t2 = -0.6666666667

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = -0.6666666667 + 6.25

Reorder the terms:
6.25 + 5t + t2 = -0.6666666667 + 6.25

Combine like terms: -0.6666666667 + 6.25 = 5.5833333333
6.25 + 5t + t2 = 5.5833333333

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 5.5833333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(t + 2.5) equal to 2.362907813 and -2.362907813.

Subproblem 1
t + 2.5 = 2.362907813

Simplifying
t + 2.5 = 2.362907813

Reorder the terms:
2.5 + t = 2.362907813

Solving
2.5 + t = 2.362907813

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 2.362907813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 2.362907813 + -2.5
t = 2.362907813 + -2.5

Combine like terms: 2.362907813 + -2.5 = -0.137092187
t = -0.137092187

Simplifying
t = -0.137092187

Subproblem 2
t + 2.5 = -2.362907813

Simplifying
t + 2.5 = -2.362907813

Reorder the terms:
2.5 + t = -2.362907813

Solving
2.5 + t = -2.362907813

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -2.362907813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -2.362907813 + -2.5
t = -2.362907813 + -2.5

Combine like terms: -2.362907813 + -2.5 = -4.862907813
t = -4.862907813

Simplifying
t = -4.862907813

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.137092187, -4.862907813}