0=(-4.9t^2)-20t+50

Solution for 0=(-4.9t^2)-20t+50 equation:

Simplifying
0 = (-4.9t2) + -20t + 50

Reorder the terms:
0 = 50 + -20t + (-4.9t2)

Solving
0 = 50 + -20t + (-4.9t2)

Solving for variable 't'.

Combine like terms: 0 + -50 = -50
-50 + 20t + (4.9t2) = 50 + -20t + (-4.9t2) + -50 + 20t + (4.9t2)

Reorder the terms:
-50 + 20t + (4.9t2) = 50 + -50 + -20t + 20t + (-4.9t2) + (4.9t2)

Combine like terms: 50 + -50 = 0
-50 + 20t + (4.9t2) = 0 + -20t + 20t + (-4.9t2) + (4.9t2)
-50 + 20t + (4.9t2) = -20t + 20t + (-4.9t2) + (4.9t2)

Combine like terms: -20t + 20t = 0
-50 + 20t + (4.9t2) = 0 + (-4.9t2) + (4.9t2)
-50 + 20t + (4.9t2) = (-4.9t2) + (4.9t2)

Combine like terms: (-4.9t2) + (4.9t2) = 0.0
-50 + 20t + (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'.
-10.20408163 + 4.081632653t + t2 = 0

Move the constant term to the right:

Add '10.20408163' to each side of the equation.
-10.20408163 + 4.081632653t + 10.20408163 + t2 = 0 + 10.20408163

Reorder the terms:
-10.20408163 + 10.20408163 + 4.081632653t + t2 = 0 + 10.20408163

Combine like terms: -10.20408163 + 10.20408163 = 0.00000000
0.00000000 + 4.081632653t + t2 = 0 + 10.20408163
4.081632653t + t2 = 0 + 10.20408163

Combine like terms: 0 + 10.20408163 = 10.20408163
4.081632653t + t2 = 10.20408163

The t term is 4.081632653t.  Take half its coefficient (2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
4.081632653t + 4.164931281 + t2 = 10.20408163 + 4.164931281

Reorder the terms:
4.164931281 + 4.081632653t + t2 = 10.20408163 + 4.164931281

Combine like terms: 10.20408163 + 4.164931281 = 14.369012911
4.164931281 + 4.081632653t + t2 = 14.369012911

Factor a perfect square on the left side:
((t) + 2.040816327)((t) + 2.040816327) = 14.369012911

Calculate the square root of the right side: 3.790648086

Break this problem into two subproblems by setting 
((t) + 2.040816327) equal to 3.790648086 and -3.790648086.

Subproblem 1
(t) + 2.040816327 = 3.790648086

Simplifying
(t) + 2.040816327 = 3.790648086
t + 2.040816327 = 3.790648086

Reorder the terms:
2.040816327 + t = 3.790648086

Solving
2.040816327 + t = 3.790648086

Solving for variable 't'.

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

Add '-2.040816327' to each side of the equation.
2.040816327 + -2.040816327 + t = 3.790648086 + -2.040816327

Combine like terms: 2.040816327 + -2.040816327 = 0.000000000
0.000000000 + t = 3.790648086 + -2.040816327
t = 3.790648086 + -2.040816327

Combine like terms: 3.790648086 + -2.040816327 = 1.749831759
t = 1.749831759

Simplifying
t = 1.749831759

Subproblem 2
(t) + 2.040816327 = -3.790648086

Simplifying
(t) + 2.040816327 = -3.790648086
t + 2.040816327 = -3.790648086

Reorder the terms:
2.040816327 + t = -3.790648086

Solving
2.040816327 + t = -3.790648086

Solving for variable 't'.

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

Add '-2.040816327' to each side of the equation.
2.040816327 + -2.040816327 + t = -3.790648086 + -2.040816327

Combine like terms: 2.040816327 + -2.040816327 = 0.000000000
0.000000000 + t = -3.790648086 + -2.040816327
t = -3.790648086 + -2.040816327

Combine like terms: -3.790648086 + -2.040816327 = -5.831464413
t = -5.831464413

Simplifying
t = -5.831464413

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.749831759, -5.831464413}