12=(38t)-(.5*9.8*(t^2))

Solution for 12=(38t)-(.5*9.8*(t^2)) equation:

Simplifying
12 = (38t) + -1(0.5 * 9.8(t2))

Multiply 0.5 * 9.8
12 = (38t) + -1(4.9t2)

Remove parenthesis around (4.9t2)
12 = (38t) + -1 * 4.9t2

Multiply -1 * 4.9
12 = (38t) + -4.9t2

Solving
12 = (38t) + -4.9t2

Solving for variable 't'.

Reorder the terms:
12 + (-38t) + 4.9t2 = (38t) + (-38t) + -4.9t2 + 4.9t2

Combine like terms: (38t) + (-38t) = 0
12 + (-38t) + 4.9t2 = 0 + -4.9t2 + 4.9t2
12 + (-38t) + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
12 + (-38t) + 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'.
2.448979592 + (-7.755102041t) + t2 = 0

Move the constant term to the right:

Add '-2.448979592' to each side of the equation.
2.448979592 + (-7.755102041t) + -2.448979592 + t2 = 0 + -2.448979592

Reorder the terms:
2.448979592 + -2.448979592 + (-7.755102041t) + t2 = 0 + -2.448979592

Combine like terms: 2.448979592 + -2.448979592 = 0.000000000
0.000000000 + (-7.755102041t) + t2 = 0 + -2.448979592
(-7.755102041t) + t2 = 0 + -2.448979592

Combine like terms: 0 + -2.448979592 = -2.448979592
(-7.755102041t) + t2 = -2.448979592

The t term is (-7.755102041t).  Take half its coefficient (-3.877551021).
Square it (15.03540192) and add it to both sides.

Add '15.03540192' to each side of the equation.
(-7.755102041t) + 15.03540192 + t2 = -2.448979592 + 15.03540192

Reorder the terms:
15.03540192 + (-7.755102041t) + t2 = -2.448979592 + 15.03540192

Combine like terms: -2.448979592 + 15.03540192 = 12.586422328
15.03540192 + (-7.755102041t) + t2 = 12.586422328

Factor a perfect square on the left side:
(t + -3.877551021)(t + -3.877551021) = 12.586422328

Calculate the square root of the right side: 3.547734816

Break this problem into two subproblems by setting 
(t + -3.877551021) equal to 3.547734816 and -3.547734816.

Subproblem 1
t + -3.877551021 = 3.547734816

Simplifying
t + -3.877551021 = 3.547734816

Reorder the terms:
-3.877551021 + t = 3.547734816

Solving
-3.877551021 + t = 3.547734816

Solving for variable 't'.

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

Add '3.877551021' to each side of the equation.
-3.877551021 + 3.877551021 + t = 3.547734816 + 3.877551021

Combine like terms: -3.877551021 + 3.877551021 = 0.000000000
0.000000000 + t = 3.547734816 + 3.877551021
t = 3.547734816 + 3.877551021

Combine like terms: 3.547734816 + 3.877551021 = 7.425285837
t = 7.425285837

Simplifying
t = 7.425285837

Subproblem 2
t + -3.877551021 = -3.547734816

Simplifying
t + -3.877551021 = -3.547734816

Reorder the terms:
-3.877551021 + t = -3.547734816

Solving
-3.877551021 + t = -3.547734816

Solving for variable 't'.

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

Add '3.877551021' to each side of the equation.
-3.877551021 + 3.877551021 + t = -3.547734816 + 3.877551021

Combine like terms: -3.877551021 + 3.877551021 = 0.000000000
0.000000000 + t = -3.547734816 + 3.877551021
t = -3.547734816 + 3.877551021

Combine like terms: -3.547734816 + 3.877551021 = 0.329816205
t = 0.329816205

Simplifying
t = 0.329816205

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.425285837, 0.329816205}