4.9t^2+3t-240=0

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Solution for 4.9t^2+3t-240=0 equation: 


Simplifying
4.9t2 + 3t + -240 = 0

Reorder the terms:
-240 + 3t + 4.9t2 = 0

Solving
-240 + 3t + 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'.
-48.97959184 + 0.612244898t + t2 = 0

Move the constant term to the right:

Add '48.97959184' to each side of the equation.
-48.97959184 + 0.612244898t + 48.97959184 + t2 = 0 + 48.97959184

Reorder the terms:
-48.97959184 + 48.97959184 + 0.612244898t + t2 = 0 + 48.97959184

Combine like terms: -48.97959184 + 48.97959184 = 0.00000000
0.00000000 + 0.612244898t + t2 = 0 + 48.97959184
0.612244898t + t2 = 0 + 48.97959184

Combine like terms: 0 + 48.97959184 = 48.97959184
0.612244898t + t2 = 48.97959184

The t term is 0.612244898t.  Take half its coefficient (0.306122449).
Square it (0.09371095378) and add it to both sides.

Add '0.09371095378' to each side of the equation.
0.612244898t + 0.09371095378 + t2 = 48.97959184 + 0.09371095378

Reorder the terms:
0.09371095378 + 0.612244898t + t2 = 48.97959184 + 0.09371095378

Combine like terms: 48.97959184 + 0.09371095378 = 49.07330279378
0.09371095378 + 0.612244898t + t2 = 49.07330279378

Factor a perfect square on the left side:
(t + 0.306122449)(t + 0.306122449) = 49.07330279378

Calculate the square root of the right side: 7.005233957

Break this problem into two subproblems by setting 
(t + 0.306122449) equal to 7.005233957 and -7.005233957.


Subproblem 1
t + 0.306122449 = 7.005233957

Simplifying
t + 0.306122449 = 7.005233957

Reorder the terms:
0.306122449 + t = 7.005233957

Solving
0.306122449 + t = 7.005233957

Solving for variable 't'.

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

Add '-0.306122449' to each side of the equation.
0.306122449 + -0.306122449 + t = 7.005233957 + -0.306122449

Combine like terms: 0.306122449 + -0.306122449 = 0.000000000
0.000000000 + t = 7.005233957 + -0.306122449
t = 7.005233957 + -0.306122449

Combine like terms: 7.005233957 + -0.306122449 = 6.699111508
t = 6.699111508

Simplifying
t = 6.699111508


Subproblem 2
t + 0.306122449 = -7.005233957

Simplifying
t + 0.306122449 = -7.005233957

Reorder the terms:
0.306122449 + t = -7.005233957

Solving
0.306122449 + t = -7.005233957

Solving for variable 't'.

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

Add '-0.306122449' to each side of the equation.
0.306122449 + -0.306122449 + t = -7.005233957 + -0.306122449

Combine like terms: 0.306122449 + -0.306122449 = 0.000000000
0.000000000 + t = -7.005233957 + -0.306122449
t = -7.005233957 + -0.306122449

Combine like terms: -7.005233957 + -0.306122449 = -7.311356406
t = -7.311356406

Simplifying
t = -7.311356406


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.699111508, -7.311356406}

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