22=-16t^2+80t

Solution for 22=-16t^2+80t equation:

Simplifying
22 = -16t2 + 80t

Reorder the terms:
22 = 80t + -16t2

Solving
22 = 80t + -16t2

Solving for variable 't'.

Reorder the terms:
22 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2

Combine like terms: 80t + -80t = 0
22 + -80t + 16t2 = 0 + -16t2 + 16t2
22 + -80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
22 + -80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -40t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -40t + 8t2)' equal to zero and attempt to solve:

Simplifying
11 + -40t + 8t2 = 0

Solving
11 + -40t + 8t2 = 0

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

Divide each side by '8'.
1.375 + -5t + t2 = 0

Move the constant term to the right:

Add '-1.375' to each side of the equation.
1.375 + -5t + -1.375 + t2 = 0 + -1.375

Reorder the terms:
1.375 + -1.375 + -5t + t2 = 0 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + -5t + t2 = 0 + -1.375
-5t + t2 = 0 + -1.375

Combine like terms: 0 + -1.375 = -1.375
-5t + t2 = -1.375

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -1.375 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -1.375 + 6.25

Combine like terms: -1.375 + 6.25 = 4.875
6.25 + -5t + t2 = 4.875

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 4.875

Calculate the square root of the right side: 2.207940217

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.207940217 and -2.207940217.

Subproblem 1
t + -2.5 = 2.207940217

Simplifying
t + -2.5 = 2.207940217

Reorder the terms:
-2.5 + t = 2.207940217

Solving
-2.5 + t = 2.207940217

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 2.207940217 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.207940217 + 2.5
t = 2.207940217 + 2.5

Combine like terms: 2.207940217 + 2.5 = 4.707940217
t = 4.707940217

Simplifying
t = 4.707940217

Subproblem 2
t + -2.5 = -2.207940217

Simplifying
t + -2.5 = -2.207940217

Reorder the terms:
-2.5 + t = -2.207940217

Solving
-2.5 + t = -2.207940217

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -2.207940217 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.207940217 + 2.5
t = -2.207940217 + 2.5

Combine like terms: -2.207940217 + 2.5 = 0.292059783
t = 0.292059783

Simplifying
t = 0.292059783

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.707940217, 0.292059783}
Solution
t = {4.707940217, 0.292059783}