5=3+8t-4.9t^2

Solution for 5=3+8t-4.9t^2 equation:

Simplifying
5 = 3 + 8t + -4.9t2

Solving
5 = 3 + 8t + -4.9t2

Solving for variable 't'.

Combine like terms: 5 + -3 = 2
2 + -8t + 4.9t2 = 3 + 8t + -4.9t2 + -3 + -8t + 4.9t2

Reorder the terms:
2 + -8t + 4.9t2 = 3 + -3 + 8t + -8t + -4.9t2 + 4.9t2

Combine like terms: 3 + -3 = 0
2 + -8t + 4.9t2 = 0 + 8t + -8t + -4.9t2 + 4.9t2
2 + -8t + 4.9t2 = 8t + -8t + -4.9t2 + 4.9t2

Combine like terms: 8t + -8t = 0
2 + -8t + 4.9t2 = 0 + -4.9t2 + 4.9t2
2 + -8t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
2 + -8t + 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'.
0.4081632653 + -1.632653061t + t2 = 0

Move the constant term to the right:

Add '-0.4081632653' to each side of the equation.
0.4081632653 + -1.632653061t + -0.4081632653 + t2 = 0 + -0.4081632653

Reorder the terms:
0.4081632653 + -0.4081632653 + -1.632653061t + t2 = 0 + -0.4081632653

Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000
0.0000000000 + -1.632653061t + t2 = 0 + -0.4081632653
-1.632653061t + t2 = 0 + -0.4081632653

Combine like terms: 0 + -0.4081632653 = -0.4081632653
-1.632653061t + t2 = -0.4081632653

The t term is -1.632653061t.  Take half its coefficient (-0.8163265305).
Square it (0.6663890044) and add it to both sides.

Add '0.6663890044' to each side of the equation.
-1.632653061t + 0.6663890044 + t2 = -0.4081632653 + 0.6663890044

Reorder the terms:
0.6663890044 + -1.632653061t + t2 = -0.4081632653 + 0.6663890044

Combine like terms: -0.4081632653 + 0.6663890044 = 0.2582257391
0.6663890044 + -1.632653061t + t2 = 0.2582257391

Factor a perfect square on the left side:
(t + -0.8163265305)(t + -0.8163265305) = 0.2582257391

Calculate the square root of the right side: 0.508159167

Break this problem into two subproblems by setting 
(t + -0.8163265305) equal to 0.508159167 and -0.508159167.

Subproblem 1
t + -0.8163265305 = 0.508159167

Simplifying
t + -0.8163265305 = 0.508159167

Reorder the terms:
-0.8163265305 + t = 0.508159167

Solving
-0.8163265305 + t = 0.508159167

Solving for variable 't'.

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

Add '0.8163265305' to each side of the equation.
-0.8163265305 + 0.8163265305 + t = 0.508159167 + 0.8163265305

Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000
0.0000000000 + t = 0.508159167 + 0.8163265305
t = 0.508159167 + 0.8163265305

Combine like terms: 0.508159167 + 0.8163265305 = 1.3244856975
t = 1.3244856975

Simplifying
t = 1.3244856975

Subproblem 2
t + -0.8163265305 = -0.508159167

Simplifying
t + -0.8163265305 = -0.508159167

Reorder the terms:
-0.8163265305 + t = -0.508159167

Solving
-0.8163265305 + t = -0.508159167

Solving for variable 't'.

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

Add '0.8163265305' to each side of the equation.
-0.8163265305 + 0.8163265305 + t = -0.508159167 + 0.8163265305

Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000
0.0000000000 + t = -0.508159167 + 0.8163265305
t = -0.508159167 + 0.8163265305

Combine like terms: -0.508159167 + 0.8163265305 = 0.3081673635
t = 0.3081673635

Simplifying
t = 0.3081673635

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.3244856975, 0.3081673635}