0=-4.9t^2+12t+0.2

Solution for 0=-4.9t^2+12t+0.2 equation:

Simplifying
0 = -4.9t2 + 12t + 0.2

Reorder the terms:
0 = 0.2 + 12t + -4.9t2

Solving
0 = 0.2 + 12t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -0.2 = -0.2
-0.2 + -12t + 4.9t2 = 0.2 + 12t + -4.9t2 + -0.2 + -12t + 4.9t2

Reorder the terms:
-0.2 + -12t + 4.9t2 = 0.2 + -0.2 + 12t + -12t + -4.9t2 + 4.9t2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + -12t + 4.9t2 = 0.0 + 12t + -12t + -4.9t2 + 4.9t2
-0.2 + -12t + 4.9t2 = 12t + -12t + -4.9t2 + 4.9t2

Combine like terms: 12t + -12t = 0
-0.2 + -12t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-0.2 + -12t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-0.2 + -12t + 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'.
-0.04081632653 + -2.448979592t + t2 = 0

Move the constant term to the right:

Add '0.04081632653' to each side of the equation.
-0.04081632653 + -2.448979592t + 0.04081632653 + t2 = 0 + 0.04081632653

Reorder the terms:
-0.04081632653 + 0.04081632653 + -2.448979592t + t2 = 0 + 0.04081632653

Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000
0.00000000000 + -2.448979592t + t2 = 0 + 0.04081632653
-2.448979592t + t2 = 0 + 0.04081632653

Combine like terms: 0 + 0.04081632653 = 0.04081632653
-2.448979592t + t2 = 0.04081632653

The t term is -2.448979592t.  Take half its coefficient (-1.224489796).
Square it (1.499375261) and add it to both sides.

Add '1.499375261' to each side of the equation.
-2.448979592t + 1.499375261 + t2 = 0.04081632653 + 1.499375261

Reorder the terms:
1.499375261 + -2.448979592t + t2 = 0.04081632653 + 1.499375261

Combine like terms: 0.04081632653 + 1.499375261 = 1.54019158753
1.499375261 + -2.448979592t + t2 = 1.54019158753

Factor a perfect square on the left side:
(t + -1.224489796)(t + -1.224489796) = 1.54019158753

Calculate the square root of the right side: 1.241044555

Break this problem into two subproblems by setting 
(t + -1.224489796) equal to 1.241044555 and -1.241044555.

Subproblem 1
t + -1.224489796 = 1.241044555

Simplifying
t + -1.224489796 = 1.241044555

Reorder the terms:
-1.224489796 + t = 1.241044555

Solving
-1.224489796 + t = 1.241044555

Solving for variable 't'.

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

Add '1.224489796' to each side of the equation.
-1.224489796 + 1.224489796 + t = 1.241044555 + 1.224489796

Combine like terms: -1.224489796 + 1.224489796 = 0.000000000
0.000000000 + t = 1.241044555 + 1.224489796
t = 1.241044555 + 1.224489796

Combine like terms: 1.241044555 + 1.224489796 = 2.465534351
t = 2.465534351

Simplifying
t = 2.465534351

Subproblem 2
t + -1.224489796 = -1.241044555

Simplifying
t + -1.224489796 = -1.241044555

Reorder the terms:
-1.224489796 + t = -1.241044555

Solving
-1.224489796 + t = -1.241044555

Solving for variable 't'.

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

Add '1.224489796' to each side of the equation.
-1.224489796 + 1.224489796 + t = -1.241044555 + 1.224489796

Combine like terms: -1.224489796 + 1.224489796 = 0.000000000
0.000000000 + t = -1.241044555 + 1.224489796
t = -1.241044555 + 1.224489796

Combine like terms: -1.241044555 + 1.224489796 = -0.016554759
t = -0.016554759

Simplifying
t = -0.016554759

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.465534351, -0.016554759}