6=1+13t-5t^2

Solution for 6=1+13t-5t^2 equation:

Simplifying
6 = 1 + 13t + -5t2

Solving
6 = 1 + 13t + -5t2

Solving for variable 't'.

Combine like terms: 6 + -1 = 5
5 + -13t + 5t2 = 1 + 13t + -5t2 + -1 + -13t + 5t2

Reorder the terms:
5 + -13t + 5t2 = 1 + -1 + 13t + -13t + -5t2 + 5t2

Combine like terms: 1 + -1 = 0
5 + -13t + 5t2 = 0 + 13t + -13t + -5t2 + 5t2
5 + -13t + 5t2 = 13t + -13t + -5t2 + 5t2

Combine like terms: 13t + -13t = 0
5 + -13t + 5t2 = 0 + -5t2 + 5t2
5 + -13t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
5 + -13t + 5t2 = 0

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

Divide each side by '5'.
1 + -2.6t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.6t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -2.6t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.6t + t2 = 0 + -1
-2.6t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.6t + t2 = -1

The t term is -2.6t.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6t + 1.69 + t2 = -1 + 1.69

Reorder the terms:
1.69 + -2.6t + t2 = -1 + 1.69

Combine like terms: -1 + 1.69 = 0.69
1.69 + -2.6t + t2 = 0.69

Factor a perfect square on the left side:
(t + -1.3)(t + -1.3) = 0.69

Calculate the square root of the right side: 0.830662386

Break this problem into two subproblems by setting 
(t + -1.3) equal to 0.830662386 and -0.830662386.

Subproblem 1
t + -1.3 = 0.830662386

Simplifying
t + -1.3 = 0.830662386

Reorder the terms:
-1.3 + t = 0.830662386

Solving
-1.3 + t = 0.830662386

Solving for variable 't'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + t = 0.830662386 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + t = 0.830662386 + 1.3
t = 0.830662386 + 1.3

Combine like terms: 0.830662386 + 1.3 = 2.130662386
t = 2.130662386

Simplifying
t = 2.130662386

Subproblem 2
t + -1.3 = -0.830662386

Simplifying
t + -1.3 = -0.830662386

Reorder the terms:
-1.3 + t = -0.830662386

Solving
-1.3 + t = -0.830662386

Solving for variable 't'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + t = -0.830662386 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + t = -0.830662386 + 1.3
t = -0.830662386 + 1.3

Combine like terms: -0.830662386 + 1.3 = 0.469337614
t = 0.469337614

Simplifying
t = 0.469337614

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.130662386, 0.469337614}