h(0)=4.9t^2+364t+339

Solution for h(0)=4.9t^2+364t+339 equation:

Simplifying
h(0) = 4.9t2 + 364t + 339

Reorder the terms for easier multiplication:
0h = 4.9t2 + 364t + 339

Anything times zero is zero.
0h = 4.9t2 + 364t + 339

Reorder the terms:
0 = 339 + 364t + 4.9t2

Solving
0 = 339 + 364t + 4.9t2

Solving for variable 't'.

Combine like terms: 0 + -339 = -339
-339 + -364t + -4.9t2 = 339 + 364t + 4.9t2 + -339 + -364t + -4.9t2

Reorder the terms:
-339 + -364t + -4.9t2 = 339 + -339 + 364t + -364t + 4.9t2 + -4.9t2

Combine like terms: 339 + -339 = 0
-339 + -364t + -4.9t2 = 0 + 364t + -364t + 4.9t2 + -4.9t2
-339 + -364t + -4.9t2 = 364t + -364t + 4.9t2 + -4.9t2

Combine like terms: 364t + -364t = 0
-339 + -364t + -4.9t2 = 0 + 4.9t2 + -4.9t2
-339 + -364t + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
-339 + -364t + -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'.
69.18367347 + 74.28571429t + t2 = 0

Move the constant term to the right:

Add '-69.18367347' to each side of the equation.
69.18367347 + 74.28571429t + -69.18367347 + t2 = 0 + -69.18367347

Reorder the terms:
69.18367347 + -69.18367347 + 74.28571429t + t2 = 0 + -69.18367347

Combine like terms: 69.18367347 + -69.18367347 = 0.00000000
0.00000000 + 74.28571429t + t2 = 0 + -69.18367347
74.28571429t + t2 = 0 + -69.18367347

Combine like terms: 0 + -69.18367347 = -69.18367347
74.28571429t + t2 = -69.18367347

The t term is 74.28571429t.  Take half its coefficient (37.14285715).
Square it (1379.591837) and add it to both sides.

Add '1379.591837' to each side of the equation.
74.28571429t + 1379.591837 + t2 = -69.18367347 + 1379.591837

Reorder the terms:
1379.591837 + 74.28571429t + t2 = -69.18367347 + 1379.591837

Combine like terms: -69.18367347 + 1379.591837 = 1310.40816353
1379.591837 + 74.28571429t + t2 = 1310.40816353

Factor a perfect square on the left side:
(t + 37.14285715)(t + 37.14285715) = 1310.40816353

Calculate the square root of the right side: 36.199560267

Break this problem into two subproblems by setting 
(t + 37.14285715) equal to 36.199560267 and -36.199560267.

Subproblem 1
t + 37.14285715 = 36.199560267

Simplifying
t + 37.14285715 = 36.199560267

Reorder the terms:
37.14285715 + t = 36.199560267

Solving
37.14285715 + t = 36.199560267

Solving for variable 't'.

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

Add '-37.14285715' to each side of the equation.
37.14285715 + -37.14285715 + t = 36.199560267 + -37.14285715

Combine like terms: 37.14285715 + -37.14285715 = 0.00000000
0.00000000 + t = 36.199560267 + -37.14285715
t = 36.199560267 + -37.14285715

Combine like terms: 36.199560267 + -37.14285715 = -0.943296883
t = -0.943296883

Simplifying
t = -0.943296883

Subproblem 2
t + 37.14285715 = -36.199560267

Simplifying
t + 37.14285715 = -36.199560267

Reorder the terms:
37.14285715 + t = -36.199560267

Solving
37.14285715 + t = -36.199560267

Solving for variable 't'.

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

Add '-37.14285715' to each side of the equation.
37.14285715 + -37.14285715 + t = -36.199560267 + -37.14285715

Combine like terms: 37.14285715 + -37.14285715 = 0.00000000
0.00000000 + t = -36.199560267 + -37.14285715
t = -36.199560267 + -37.14285715

Combine like terms: -36.199560267 + -37.14285715 = -73.342417417
t = -73.342417417

Simplifying
t = -73.342417417

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.943296883, -73.342417417}