33.8=26t+20t^2

Solution for 33.8=26t+20t^2 equation:

Simplifying
33.8 = 26t + 20t2

Solving
33.8 = 26t + 20t2

Solving for variable 't'.

Reorder the terms:
33.8 + -26t + -20t2 = 26t + -26t + 20t2 + -20t2

Combine like terms: 26t + -26t = 0
33.8 + -26t + -20t2 = 0 + 20t2 + -20t2
33.8 + -26t + -20t2 = 20t2 + -20t2

Combine like terms: 20t2 + -20t2 = 0
33.8 + -26t + -20t2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-1.69 + 1.3t + t2 = 0

Move the constant term to the right:

Add '1.69' to each side of the equation.
-1.69 + 1.3t + 1.69 + t2 = 0 + 1.69

Reorder the terms:
-1.69 + 1.69 + 1.3t + t2 = 0 + 1.69

Combine like terms: -1.69 + 1.69 = 0.00
0.00 + 1.3t + t2 = 0 + 1.69
1.3t + t2 = 0 + 1.69

Combine like terms: 0 + 1.69 = 1.69
1.3t + t2 = 1.69

The t term is 1.3t.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3t + 0.4225 + t2 = 1.69 + 0.4225

Reorder the terms:
0.4225 + 1.3t + t2 = 1.69 + 0.4225

Combine like terms: 1.69 + 0.4225 = 2.1125
0.4225 + 1.3t + t2 = 2.1125

Factor a perfect square on the left side:
(t + 0.65)(t + 0.65) = 2.1125

Calculate the square root of the right side: 1.453444185

Break this problem into two subproblems by setting 
(t + 0.65) equal to 1.453444185 and -1.453444185.

Subproblem 1
t + 0.65 = 1.453444185

Simplifying
t + 0.65 = 1.453444185

Reorder the terms:
0.65 + t = 1.453444185

Solving
0.65 + t = 1.453444185

Solving for variable 't'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + t = 1.453444185 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + t = 1.453444185 + -0.65
t = 1.453444185 + -0.65

Combine like terms: 1.453444185 + -0.65 = 0.803444185
t = 0.803444185

Simplifying
t = 0.803444185

Subproblem 2
t + 0.65 = -1.453444185

Simplifying
t + 0.65 = -1.453444185

Reorder the terms:
0.65 + t = -1.453444185

Solving
0.65 + t = -1.453444185

Solving for variable 't'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + t = -1.453444185 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + t = -1.453444185 + -0.65
t = -1.453444185 + -0.65

Combine like terms: -1.453444185 + -0.65 = -2.103444185
t = -2.103444185

Simplifying
t = -2.103444185

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.803444185, -2.103444185}