-16t^2+3t+1.3=0

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Solution for -16t^2+3t+1.3=0 equation: 


Simplifying
-16t2 + 3t + 1.3 = 0

Reorder the terms:
1.3 + 3t + -16t2 = 0

Solving
1.3 + 3t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.08125 + -0.1875t + t2 = 0

Move the constant term to the right:

Add '0.08125' to each side of the equation.
-0.08125 + -0.1875t + 0.08125 + t2 = 0 + 0.08125

Reorder the terms:
-0.08125 + 0.08125 + -0.1875t + t2 = 0 + 0.08125

Combine like terms: -0.08125 + 0.08125 = 0.00000
0.00000 + -0.1875t + t2 = 0 + 0.08125
-0.1875t + t2 = 0 + 0.08125

Combine like terms: 0 + 0.08125 = 0.08125
-0.1875t + t2 = 0.08125

The t term is -0.1875t.  Take half its coefficient (-0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
-0.1875t + 0.0087890625 + t2 = 0.08125 + 0.0087890625

Reorder the terms:
0.0087890625 + -0.1875t + t2 = 0.08125 + 0.0087890625

Combine like terms: 0.08125 + 0.0087890625 = 0.0900390625
0.0087890625 + -0.1875t + t2 = 0.0900390625

Factor a perfect square on the left side:
(t + -0.09375)(t + -0.09375) = 0.0900390625

Calculate the square root of the right side: 0.300065097

Break this problem into two subproblems by setting 
(t + -0.09375) equal to 0.300065097 and -0.300065097.


Subproblem 1
t + -0.09375 = 0.300065097

Simplifying
t + -0.09375 = 0.300065097

Reorder the terms:
-0.09375 + t = 0.300065097

Solving
-0.09375 + t = 0.300065097

Solving for variable 't'.

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

Add '0.09375' to each side of the equation.
-0.09375 + 0.09375 + t = 0.300065097 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + t = 0.300065097 + 0.09375
t = 0.300065097 + 0.09375

Combine like terms: 0.300065097 + 0.09375 = 0.393815097
t = 0.393815097

Simplifying
t = 0.393815097


Subproblem 2
t + -0.09375 = -0.300065097

Simplifying
t + -0.09375 = -0.300065097

Reorder the terms:
-0.09375 + t = -0.300065097

Solving
-0.09375 + t = -0.300065097

Solving for variable 't'.

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

Add '0.09375' to each side of the equation.
-0.09375 + 0.09375 + t = -0.300065097 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + t = -0.300065097 + 0.09375
t = -0.300065097 + 0.09375

Combine like terms: -0.300065097 + 0.09375 = -0.206315097
t = -0.206315097

Simplifying
t = -0.206315097


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.393815097, -0.206315097}

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