1.3t(t+8.2)=37.5

Solution for 1.3t(t+8.2)=37.5 equation:

Simplifying
1.3t(t + 8.2) = 37.5

Reorder the terms:
1.3t(8.2 + t) = 37.5
(8.2 * 1.3t + t * 1.3t) = 37.5
(10.66t + 1.3t2) = 37.5

Solving
10.66t + 1.3t2 = 37.5

Solving for variable 't'.

Reorder the terms:
-37.5 + 10.66t + 1.3t2 = 37.5 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
-37.5 + 10.66t + 1.3t2 = 0.0

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

Divide each side by '1.3'.
-28.84615385 + 8.2t + t2 = 0

Move the constant term to the right:

Add '28.84615385' to each side of the equation.
-28.84615385 + 8.2t + 28.84615385 + t2 = 0 + 28.84615385

Reorder the terms:
-28.84615385 + 28.84615385 + 8.2t + t2 = 0 + 28.84615385

Combine like terms: -28.84615385 + 28.84615385 = 0.00000000
0.00000000 + 8.2t + t2 = 0 + 28.84615385
8.2t + t2 = 0 + 28.84615385

Combine like terms: 0 + 28.84615385 = 28.84615385
8.2t + t2 = 28.84615385

The t term is 8.2t.  Take half its coefficient (4.1).
Square it (16.81) and add it to both sides.

Add '16.81' to each side of the equation.
8.2t + 16.81 + t2 = 28.84615385 + 16.81

Reorder the terms:
16.81 + 8.2t + t2 = 28.84615385 + 16.81

Combine like terms: 28.84615385 + 16.81 = 45.65615385
16.81 + 8.2t + t2 = 45.65615385

Factor a perfect square on the left side:
(t + 4.1)(t + 4.1) = 45.65615385

Calculate the square root of the right side: 6.756933761

Break this problem into two subproblems by setting 
(t + 4.1) equal to 6.756933761 and -6.756933761.

Subproblem 1
t + 4.1 = 6.756933761

Simplifying
t + 4.1 = 6.756933761

Reorder the terms:
4.1 + t = 6.756933761

Solving
4.1 + t = 6.756933761

Solving for variable 't'.

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

Add '-4.1' to each side of the equation.
4.1 + -4.1 + t = 6.756933761 + -4.1

Combine like terms: 4.1 + -4.1 = 0.0
0.0 + t = 6.756933761 + -4.1
t = 6.756933761 + -4.1

Combine like terms: 6.756933761 + -4.1 = 2.656933761
t = 2.656933761

Simplifying
t = 2.656933761

Subproblem 2
t + 4.1 = -6.756933761

Simplifying
t + 4.1 = -6.756933761

Reorder the terms:
4.1 + t = -6.756933761

Solving
4.1 + t = -6.756933761

Solving for variable 't'.

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

Add '-4.1' to each side of the equation.
4.1 + -4.1 + t = -6.756933761 + -4.1

Combine like terms: 4.1 + -4.1 = 0.0
0.0 + t = -6.756933761 + -4.1
t = -6.756933761 + -4.1

Combine like terms: -6.756933761 + -4.1 = -10.856933761
t = -10.856933761

Simplifying
t = -10.856933761

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.656933761, -10.856933761}