-4.9t^2+9.8t-3.675=0

Solution for -4.9t^2+9.8t-3.675=0 equation:

Simplifying
-4.9t2 + 9.8t + -3.675 = 0

Reorder the terms:
-3.675 + 9.8t + -4.9t2 = 0

Solving
-3.675 + 9.8t + -4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '-4.9'.
0.75 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2t + -0.75 + t2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2t + t2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2t + t2 = 0 + -0.75
-2t + t2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2t + t2 = -0.75

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.75 + 1

Reorder the terms:
1 + -2t + t2 = -0.75 + 1

Combine like terms: -0.75 + 1 = 0.25
1 + -2t + t2 = 0.25

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(t + -1) equal to 0.5 and -0.5.

Subproblem 1
t + -1 = 0.5

Simplifying
t + -1 = 0.5

Reorder the terms:
-1 + t = 0.5

Solving
-1 + t = 0.5

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.5 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.5 + 1
t = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
t = 1.5

Simplifying
t = 1.5

Subproblem 2
t + -1 = -0.5

Simplifying
t + -1 = -0.5

Reorder the terms:
-1 + t = -0.5

Solving
-1 + t = -0.5

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.5 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.5 + 1
t = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
t = 0.5

Simplifying
t = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.5, 0.5}