6=3+9t-5t^2

Solution for 6=3+9t-5t^2 equation:

Simplifying
6 = 3 + 9t + -5t2

Solving
6 = 3 + 9t + -5t2

Solving for variable 't'.

Combine like terms: 6 + -3 = 3
3 + -9t + 5t2 = 3 + 9t + -5t2 + -3 + -9t + 5t2

Reorder the terms:
3 + -9t + 5t2 = 3 + -3 + 9t + -9t + -5t2 + 5t2

Combine like terms: 3 + -3 = 0
3 + -9t + 5t2 = 0 + 9t + -9t + -5t2 + 5t2
3 + -9t + 5t2 = 9t + -9t + -5t2 + 5t2

Combine like terms: 9t + -9t = 0
3 + -9t + 5t2 = 0 + -5t2 + 5t2
3 + -9t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
3 + -9t + 5t2 = 0

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

Divide each side by '5'.
0.6 + -1.8t + t2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.8t + -0.6 + t2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.8t + t2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.8t + t2 = 0 + -0.6
-1.8t + t2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.8t + t2 = -0.6

The t term is -1.8t.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8t + 0.81 + t2 = -0.6 + 0.81

Reorder the terms:
0.81 + -1.8t + t2 = -0.6 + 0.81

Combine like terms: -0.6 + 0.81 = 0.21
0.81 + -1.8t + t2 = 0.21

Factor a perfect square on the left side:
(t + -0.9)(t + -0.9) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(t + -0.9) equal to 0.458257569 and -0.458257569.

Subproblem 1
t + -0.9 = 0.458257569

Simplifying
t + -0.9 = 0.458257569

Reorder the terms:
-0.9 + t = 0.458257569

Solving
-0.9 + t = 0.458257569

Solving for variable 't'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + t = 0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + t = 0.458257569 + 0.9
t = 0.458257569 + 0.9

Combine like terms: 0.458257569 + 0.9 = 1.358257569
t = 1.358257569

Simplifying
t = 1.358257569

Subproblem 2
t + -0.9 = -0.458257569

Simplifying
t + -0.9 = -0.458257569

Reorder the terms:
-0.9 + t = -0.458257569

Solving
-0.9 + t = -0.458257569

Solving for variable 't'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + t = -0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + t = -0.458257569 + 0.9
t = -0.458257569 + 0.9

Combine like terms: -0.458257569 + 0.9 = 0.441742431
t = 0.441742431

Simplifying
t = 0.441742431

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.358257569, 0.441742431}