-4.9t^2+12t-1=0

Solution for -4.9t^2+12t-1=0 equation:

Simplifying
-4.9t2 + 12t + -1 = 0

Reorder the terms:
-1 + 12t + -4.9t2 = 0

Solving
-1 + 12t + -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'.
0.2040816327 + -2.448979592t + t2 = 0

Move the constant term to the right:

Add '-0.2040816327' to each side of the equation.
0.2040816327 + -2.448979592t + -0.2040816327 + t2 = 0 + -0.2040816327

Reorder the terms:
0.2040816327 + -0.2040816327 + -2.448979592t + t2 = 0 + -0.2040816327

Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000
0.0000000000 + -2.448979592t + t2 = 0 + -0.2040816327
-2.448979592t + t2 = 0 + -0.2040816327

Combine like terms: 0 + -0.2040816327 = -0.2040816327
-2.448979592t + t2 = -0.2040816327

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 = -0.2040816327 + 1.499375261

Reorder the terms:
1.499375261 + -2.448979592t + t2 = -0.2040816327 + 1.499375261

Combine like terms: -0.2040816327 + 1.499375261 = 1.2952936283
1.499375261 + -2.448979592t + t2 = 1.2952936283

Factor a perfect square on the left side:
(t + -1.224489796)(t + -1.224489796) = 1.2952936283

Calculate the square root of the right side: 1.138109673

Break this problem into two subproblems by setting 
(t + -1.224489796) equal to 1.138109673 and -1.138109673.

Subproblem 1
t + -1.224489796 = 1.138109673

Simplifying
t + -1.224489796 = 1.138109673

Reorder the terms:
-1.224489796 + t = 1.138109673

Solving
-1.224489796 + t = 1.138109673

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 = 1.138109673 + 1.224489796

Combine like terms: -1.224489796 + 1.224489796 = 0.000000000
0.000000000 + t = 1.138109673 + 1.224489796
t = 1.138109673 + 1.224489796

Combine like terms: 1.138109673 + 1.224489796 = 2.362599469
t = 2.362599469

Simplifying
t = 2.362599469

Subproblem 2
t + -1.224489796 = -1.138109673

Simplifying
t + -1.224489796 = -1.138109673

Reorder the terms:
-1.224489796 + t = -1.138109673

Solving
-1.224489796 + t = -1.138109673

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 = -1.138109673 + 1.224489796

Combine like terms: -1.224489796 + 1.224489796 = 0.000000000
0.000000000 + t = -1.138109673 + 1.224489796
t = -1.138109673 + 1.224489796

Combine like terms: -1.138109673 + 1.224489796 = 0.086380123
t = 0.086380123

Simplifying
t = 0.086380123

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.362599469, 0.086380123}