-18.5=19.04t+.5(-9.8)t^2

Solution for -18.5=19.04t+.5(-9.8)t^2 equation:

Simplifying
-18.5 = 19.04t + 0.5(-9.8) * t2

Multiply 0.5 * -9.8
-18.5 = 19.04t + -4.9t2

Solving
-18.5 = 19.04t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-18.5 + -19.04t + 4.9t2 = 19.04t + -19.04t + -4.9t2 + 4.9t2

Combine like terms: 19.04t + -19.04t = 0.00
-18.5 + -19.04t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2
-18.5 + -19.04t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-18.5 + -19.04t + 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'.
-3.775510204 + -3.885714286t + t2 = 0

Move the constant term to the right:

Add '3.775510204' to each side of the equation.
-3.775510204 + -3.885714286t + 3.775510204 + t2 = 0 + 3.775510204

Reorder the terms:
-3.775510204 + 3.775510204 + -3.885714286t + t2 = 0 + 3.775510204

Combine like terms: -3.775510204 + 3.775510204 = 0.000000000
0.000000000 + -3.885714286t + t2 = 0 + 3.775510204
-3.885714286t + t2 = 0 + 3.775510204

Combine like terms: 0 + 3.775510204 = 3.775510204
-3.885714286t + t2 = 3.775510204

The t term is -3.885714286t.  Take half its coefficient (-1.942857143).
Square it (3.774693878) and add it to both sides.

Add '3.774693878' to each side of the equation.
-3.885714286t + 3.774693878 + t2 = 3.775510204 + 3.774693878

Reorder the terms:
3.774693878 + -3.885714286t + t2 = 3.775510204 + 3.774693878

Combine like terms: 3.775510204 + 3.774693878 = 7.550204082
3.774693878 + -3.885714286t + t2 = 7.550204082

Factor a perfect square on the left side:
(t + -1.942857143)(t + -1.942857143) = 7.550204082

Calculate the square root of the right side: 2.747763469

Break this problem into two subproblems by setting 
(t + -1.942857143) equal to 2.747763469 and -2.747763469.

Subproblem 1
t + -1.942857143 = 2.747763469

Simplifying
t + -1.942857143 = 2.747763469

Reorder the terms:
-1.942857143 + t = 2.747763469

Solving
-1.942857143 + t = 2.747763469

Solving for variable 't'.

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

Add '1.942857143' to each side of the equation.
-1.942857143 + 1.942857143 + t = 2.747763469 + 1.942857143

Combine like terms: -1.942857143 + 1.942857143 = 0.000000000
0.000000000 + t = 2.747763469 + 1.942857143
t = 2.747763469 + 1.942857143

Combine like terms: 2.747763469 + 1.942857143 = 4.690620612
t = 4.690620612

Simplifying
t = 4.690620612

Subproblem 2
t + -1.942857143 = -2.747763469

Simplifying
t + -1.942857143 = -2.747763469

Reorder the terms:
-1.942857143 + t = -2.747763469

Solving
-1.942857143 + t = -2.747763469

Solving for variable 't'.

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

Add '1.942857143' to each side of the equation.
-1.942857143 + 1.942857143 + t = -2.747763469 + 1.942857143

Combine like terms: -1.942857143 + 1.942857143 = 0.000000000
0.000000000 + t = -2.747763469 + 1.942857143
t = -2.747763469 + 1.942857143

Combine like terms: -2.747763469 + 1.942857143 = -0.804906326
t = -0.804906326

Simplifying
t = -0.804906326

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.690620612, -0.804906326}