5.5=-2.7t^2+30t+6.5

Solution for 5.5=-2.7t^2+30t+6.5 equation:

Simplifying
5.5 = -2.7t2 + 30t + 6.5

Reorder the terms:
5.5 = 6.5 + 30t + -2.7t2

Solving
5.5 = 6.5 + 30t + -2.7t2

Solving for variable 't'.

Combine like terms: 5.5 + -6.5 = -1
-1 + -30t + 2.7t2 = 6.5 + 30t + -2.7t2 + -6.5 + -30t + 2.7t2

Reorder the terms:
-1 + -30t + 2.7t2 = 6.5 + -6.5 + 30t + -30t + -2.7t2 + 2.7t2

Combine like terms: 6.5 + -6.5 = 0.0
-1 + -30t + 2.7t2 = 0.0 + 30t + -30t + -2.7t2 + 2.7t2
-1 + -30t + 2.7t2 = 30t + -30t + -2.7t2 + 2.7t2

Combine like terms: 30t + -30t = 0
-1 + -30t + 2.7t2 = 0 + -2.7t2 + 2.7t2
-1 + -30t + 2.7t2 = -2.7t2 + 2.7t2

Combine like terms: -2.7t2 + 2.7t2 = 0.0
-1 + -30t + 2.7t2 = 0.0

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

Divide each side by '2.7'.
-0.3703703704 + -11.11111111t + t2 = 0

Move the constant term to the right:

Add '0.3703703704' to each side of the equation.
-0.3703703704 + -11.11111111t + 0.3703703704 + t2 = 0 + 0.3703703704

Reorder the terms:
-0.3703703704 + 0.3703703704 + -11.11111111t + t2 = 0 + 0.3703703704

Combine like terms: -0.3703703704 + 0.3703703704 = 0.0000000000
0.0000000000 + -11.11111111t + t2 = 0 + 0.3703703704
-11.11111111t + t2 = 0 + 0.3703703704

Combine like terms: 0 + 0.3703703704 = 0.3703703704
-11.11111111t + t2 = 0.3703703704

The t term is -11.11111111t.  Take half its coefficient (-5.555555555).
Square it (30.86419752) and add it to both sides.

Add '30.86419752' to each side of the equation.
-11.11111111t + 30.86419752 + t2 = 0.3703703704 + 30.86419752

Reorder the terms:
30.86419752 + -11.11111111t + t2 = 0.3703703704 + 30.86419752

Combine like terms: 0.3703703704 + 30.86419752 = 31.2345678904
30.86419752 + -11.11111111t + t2 = 31.2345678904

Factor a perfect square on the left side:
(t + -5.555555555)(t + -5.555555555) = 31.2345678904

Calculate the square root of the right side: 5.588789483

Break this problem into two subproblems by setting 
(t + -5.555555555) equal to 5.588789483 and -5.588789483.

Subproblem 1
t + -5.555555555 = 5.588789483

Simplifying
t + -5.555555555 = 5.588789483

Reorder the terms:
-5.555555555 + t = 5.588789483

Solving
-5.555555555 + t = 5.588789483

Solving for variable 't'.

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

Add '5.555555555' to each side of the equation.
-5.555555555 + 5.555555555 + t = 5.588789483 + 5.555555555

Combine like terms: -5.555555555 + 5.555555555 = 0.000000000
0.000000000 + t = 5.588789483 + 5.555555555
t = 5.588789483 + 5.555555555

Combine like terms: 5.588789483 + 5.555555555 = 11.144345038
t = 11.144345038

Simplifying
t = 11.144345038

Subproblem 2
t + -5.555555555 = -5.588789483

Simplifying
t + -5.555555555 = -5.588789483

Reorder the terms:
-5.555555555 + t = -5.588789483

Solving
-5.555555555 + t = -5.588789483

Solving for variable 't'.

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

Add '5.555555555' to each side of the equation.
-5.555555555 + 5.555555555 + t = -5.588789483 + 5.555555555

Combine like terms: -5.555555555 + 5.555555555 = 0.000000000
0.000000000 + t = -5.588789483 + 5.555555555
t = -5.588789483 + 5.555555555

Combine like terms: -5.588789483 + 5.555555555 = -0.033233928
t = -0.033233928

Simplifying
t = -0.033233928

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.144345038, -0.033233928}