-20=16.9t-4.9t^2

Solution for -20=16.9t-4.9t^2 equation:

Simplifying
-20 = 16.9t + -4.9t2

Solving
-20 = 16.9t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-20 + -16.9t + 4.9t2 = 16.9t + -16.9t + -4.9t2 + 4.9t2

Combine like terms: 16.9t + -16.9t = 0.0
-20 + -16.9t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-20 + -16.9t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-20 + -16.9t + 4.9t2 = 0.0

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

Divide each side by '4.9'.
-4.081632653 + -3.448979592t + t2 = 0

Move the constant term to the right:

Add '4.081632653' to each side of the equation.
-4.081632653 + -3.448979592t + 4.081632653 + t2 = 0 + 4.081632653

Reorder the terms:
-4.081632653 + 4.081632653 + -3.448979592t + t2 = 0 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + -3.448979592t + t2 = 0 + 4.081632653
-3.448979592t + t2 = 0 + 4.081632653

Combine like terms: 0 + 4.081632653 = 4.081632653
-3.448979592t + t2 = 4.081632653

The t term is -3.448979592t.  Take half its coefficient (-1.724489796).
Square it (2.973865057) and add it to both sides.

Add '2.973865057' to each side of the equation.
-3.448979592t + 2.973865057 + t2 = 4.081632653 + 2.973865057

Reorder the terms:
2.973865057 + -3.448979592t + t2 = 4.081632653 + 2.973865057

Combine like terms: 4.081632653 + 2.973865057 = 7.05549771
2.973865057 + -3.448979592t + t2 = 7.05549771

Factor a perfect square on the left side:
(t + -1.724489796)(t + -1.724489796) = 7.05549771

Calculate the square root of the right side: 2.656218686

Break this problem into two subproblems by setting 
(t + -1.724489796) equal to 2.656218686 and -2.656218686.

Subproblem 1
t + -1.724489796 = 2.656218686

Simplifying
t + -1.724489796 = 2.656218686

Reorder the terms:
-1.724489796 + t = 2.656218686

Solving
-1.724489796 + t = 2.656218686

Solving for variable 't'.

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

Add '1.724489796' to each side of the equation.
-1.724489796 + 1.724489796 + t = 2.656218686 + 1.724489796

Combine like terms: -1.724489796 + 1.724489796 = 0.000000000
0.000000000 + t = 2.656218686 + 1.724489796
t = 2.656218686 + 1.724489796

Combine like terms: 2.656218686 + 1.724489796 = 4.380708482
t = 4.380708482

Simplifying
t = 4.380708482

Subproblem 2
t + -1.724489796 = -2.656218686

Simplifying
t + -1.724489796 = -2.656218686

Reorder the terms:
-1.724489796 + t = -2.656218686

Solving
-1.724489796 + t = -2.656218686

Solving for variable 't'.

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

Add '1.724489796' to each side of the equation.
-1.724489796 + 1.724489796 + t = -2.656218686 + 1.724489796

Combine like terms: -1.724489796 + 1.724489796 = 0.000000000
0.000000000 + t = -2.656218686 + 1.724489796
t = -2.656218686 + 1.724489796

Combine like terms: -2.656218686 + 1.724489796 = -0.93172889
t = -0.93172889

Simplifying
t = -0.93172889

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.380708482, -0.93172889}