0=1.85t^2+30t+6

Solution for 0=1.85t^2+30t+6 equation:

Simplifying
0 = 1.85t2 + 30t + 6

Reorder the terms:
0 = 6 + 30t + 1.85t2

Solving
0 = 6 + 30t + 1.85t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -30t + -1.85t2 = 6 + 30t + 1.85t2 + -6 + -30t + -1.85t2

Reorder the terms:
-6 + -30t + -1.85t2 = 6 + -6 + 30t + -30t + 1.85t2 + -1.85t2

Combine like terms: 6 + -6 = 0
-6 + -30t + -1.85t2 = 0 + 30t + -30t + 1.85t2 + -1.85t2
-6 + -30t + -1.85t2 = 30t + -30t + 1.85t2 + -1.85t2

Combine like terms: 30t + -30t = 0
-6 + -30t + -1.85t2 = 0 + 1.85t2 + -1.85t2
-6 + -30t + -1.85t2 = 1.85t2 + -1.85t2

Combine like terms: 1.85t2 + -1.85t2 = 0.00
-6 + -30t + -1.85t2 = 0.00

Begin completing the square.  Divide all terms by
-1.85 the coefficient of the squared term: 

Divide each side by '-1.85'.
3.243243243 + 16.21621622t + t2 = 0

Move the constant term to the right:

Add '-3.243243243' to each side of the equation.
3.243243243 + 16.21621622t + -3.243243243 + t2 = 0 + -3.243243243

Reorder the terms:
3.243243243 + -3.243243243 + 16.21621622t + t2 = 0 + -3.243243243

Combine like terms: 3.243243243 + -3.243243243 = 0.000000000
0.000000000 + 16.21621622t + t2 = 0 + -3.243243243
16.21621622t + t2 = 0 + -3.243243243

Combine like terms: 0 + -3.243243243 = -3.243243243
16.21621622t + t2 = -3.243243243

The t term is 16.21621622t.  Take half its coefficient (8.10810811).
Square it (65.74141712) and add it to both sides.

Add '65.74141712' to each side of the equation.
16.21621622t + 65.74141712 + t2 = -3.243243243 + 65.74141712

Reorder the terms:
65.74141712 + 16.21621622t + t2 = -3.243243243 + 65.74141712

Combine like terms: -3.243243243 + 65.74141712 = 62.498173877
65.74141712 + 16.21621622t + t2 = 62.498173877

Factor a perfect square on the left side:
(t + 8.10810811)(t + 8.10810811) = 62.498173877

Calculate the square root of the right side: 7.905578655

Break this problem into two subproblems by setting 
(t + 8.10810811) equal to 7.905578655 and -7.905578655.

Subproblem 1
t + 8.10810811 = 7.905578655

Simplifying
t + 8.10810811 = 7.905578655

Reorder the terms:
8.10810811 + t = 7.905578655

Solving
8.10810811 + t = 7.905578655

Solving for variable 't'.

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

Add '-8.10810811' to each side of the equation.
8.10810811 + -8.10810811 + t = 7.905578655 + -8.10810811

Combine like terms: 8.10810811 + -8.10810811 = 0.00000000
0.00000000 + t = 7.905578655 + -8.10810811
t = 7.905578655 + -8.10810811

Combine like terms: 7.905578655 + -8.10810811 = -0.202529455
t = -0.202529455

Simplifying
t = -0.202529455

Subproblem 2
t + 8.10810811 = -7.905578655

Simplifying
t + 8.10810811 = -7.905578655

Reorder the terms:
8.10810811 + t = -7.905578655

Solving
8.10810811 + t = -7.905578655

Solving for variable 't'.

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

Add '-8.10810811' to each side of the equation.
8.10810811 + -8.10810811 + t = -7.905578655 + -8.10810811

Combine like terms: 8.10810811 + -8.10810811 = 0.00000000
0.00000000 + t = -7.905578655 + -8.10810811
t = -7.905578655 + -8.10810811

Combine like terms: -7.905578655 + -8.10810811 = -16.013686765
t = -16.013686765

Simplifying
t = -16.013686765

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.202529455, -16.013686765}