2+14t-4.9t^2=0

Solution for 2+14t-4.9t^2=0 equation:

Simplifying
2 + 14t + -4.9t2 = 0

Solving
2 + 14t + -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'.
-0.4081632653 + -2.857142857t + t2 = 0

Move the constant term to the right:

Add '0.4081632653' to each side of the equation.
-0.4081632653 + -2.857142857t + 0.4081632653 + t2 = 0 + 0.4081632653

Reorder the terms:
-0.4081632653 + 0.4081632653 + -2.857142857t + t2 = 0 + 0.4081632653

Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000
0.0000000000 + -2.857142857t + t2 = 0 + 0.4081632653
-2.857142857t + t2 = 0 + 0.4081632653

Combine like terms: 0 + 0.4081632653 = 0.4081632653
-2.857142857t + t2 = 0.4081632653

The t term is -2.857142857t.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857t + 2.040816328 + t2 = 0.4081632653 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857t + t2 = 0.4081632653 + 2.040816328

Combine like terms: 0.4081632653 + 2.040816328 = 2.4489795933
2.040816328 + -2.857142857t + t2 = 2.4489795933

Factor a perfect square on the left side:
(t + -1.428571429)(t + -1.428571429) = 2.4489795933

Calculate the square root of the right side: 1.564921593

Break this problem into two subproblems by setting 
(t + -1.428571429) equal to 1.564921593 and -1.564921593.

Subproblem 1
t + -1.428571429 = 1.564921593

Simplifying
t + -1.428571429 = 1.564921593

Reorder the terms:
-1.428571429 + t = 1.564921593

Solving
-1.428571429 + t = 1.564921593

Solving for variable 't'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + t = 1.564921593 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + t = 1.564921593 + 1.428571429
t = 1.564921593 + 1.428571429

Combine like terms: 1.564921593 + 1.428571429 = 2.993493022
t = 2.993493022

Simplifying
t = 2.993493022

Subproblem 2
t + -1.428571429 = -1.564921593

Simplifying
t + -1.428571429 = -1.564921593

Reorder the terms:
-1.428571429 + t = -1.564921593

Solving
-1.428571429 + t = -1.564921593

Solving for variable 't'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + t = -1.564921593 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + t = -1.564921593 + 1.428571429
t = -1.564921593 + 1.428571429

Combine like terms: -1.564921593 + 1.428571429 = -0.136350164
t = -0.136350164

Simplifying
t = -0.136350164

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.993493022, -0.136350164}