-4.9t^2+3t+1.5=0

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Solution for -4.9t^2+3t+1.5=0 equation: 


Simplifying
-4.9t2 + 3t + 1.5 = 0

Reorder the terms:
1.5 + 3t + -4.9t2 = 0

Solving
1.5 + 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'.
-0.306122449 + -0.612244898t + t2 = 0

Move the constant term to the right:

Add '0.306122449' to each side of the equation.
-0.306122449 + -0.612244898t + 0.306122449 + t2 = 0 + 0.306122449

Reorder the terms:
-0.306122449 + 0.306122449 + -0.612244898t + t2 = 0 + 0.306122449

Combine like terms: -0.306122449 + 0.306122449 = 0.000000000
0.000000000 + -0.612244898t + t2 = 0 + 0.306122449
-0.612244898t + t2 = 0 + 0.306122449

Combine like terms: 0 + 0.306122449 = 0.306122449
-0.612244898t + t2 = 0.306122449

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 = 0.306122449 + 0.09371095378

Reorder the terms:
0.09371095378 + -0.612244898t + t2 = 0.306122449 + 0.09371095378

Combine like terms: 0.306122449 + 0.09371095378 = 0.39983340278
0.09371095378 + -0.612244898t + t2 = 0.39983340278

Factor a perfect square on the left side:
(t + -0.306122449)(t + -0.306122449) = 0.39983340278

Calculate the square root of the right side: 0.632323812

Break this problem into two subproblems by setting 
(t + -0.306122449) equal to 0.632323812 and -0.632323812.


Subproblem 1
t + -0.306122449 = 0.632323812

Simplifying
t + -0.306122449 = 0.632323812

Reorder the terms:
-0.306122449 + t = 0.632323812

Solving
-0.306122449 + t = 0.632323812

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 = 0.632323812 + 0.306122449

Combine like terms: -0.306122449 + 0.306122449 = 0.000000000
0.000000000 + t = 0.632323812 + 0.306122449
t = 0.632323812 + 0.306122449

Combine like terms: 0.632323812 + 0.306122449 = 0.938446261
t = 0.938446261

Simplifying
t = 0.938446261


Subproblem 2
t + -0.306122449 = -0.632323812

Simplifying
t + -0.306122449 = -0.632323812

Reorder the terms:
-0.306122449 + t = -0.632323812

Solving
-0.306122449 + t = -0.632323812

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 = -0.632323812 + 0.306122449

Combine like terms: -0.306122449 + 0.306122449 = 0.000000000
0.000000000 + t = -0.632323812 + 0.306122449
t = -0.632323812 + 0.306122449

Combine like terms: -0.632323812 + 0.306122449 = -0.326201363
t = -0.326201363

Simplifying
t = -0.326201363


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.938446261, -0.326201363}

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