-16t^2+3t+1.3=.5

Solution for -16t^2+3t+1.3=.5 equation:

Simplifying
-16t2 + 3t + 1.3 = 0.5

Reorder the terms:
1.3 + 3t + -16t2 = 0.5

Solving
1.3 + 3t + -16t2 = 0.5

Solving for variable 't'.

Reorder the terms:
1.3 + -0.5 + 3t + -16t2 = 0.5 + -0.5

Combine like terms: 1.3 + -0.5 = 0.8
0.8 + 3t + -16t2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.8 + 3t + -16t2 = 0.0

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

Divide each side by '-16'.
-0.05 + -0.1875t + t2 = 0.0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -0.1875t + 0.05 + t2 = 0.0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -0.1875t + t2 = 0.0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -0.1875t + t2 = 0.0 + 0.05
-0.1875t + t2 = 0.0 + 0.05

Combine like terms: 0.0 + 0.05 = 0.05
-0.1875t + t2 = 0.05

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 = 0.05 + 0.0087890625

Reorder the terms:
0.0087890625 + -0.1875t + t2 = 0.05 + 0.0087890625

Combine like terms: 0.05 + 0.0087890625 = 0.0587890625
0.0087890625 + -0.1875t + t2 = 0.0587890625

Factor a perfect square on the left side:
(t + -0.09375)(t + -0.09375) = 0.0587890625

Calculate the square root of the right side: 0.242464559

Break this problem into two subproblems by setting 
(t + -0.09375) equal to 0.242464559 and -0.242464559.

Subproblem 1
t + -0.09375 = 0.242464559

Simplifying
t + -0.09375 = 0.242464559

Reorder the terms:
-0.09375 + t = 0.242464559

Solving
-0.09375 + t = 0.242464559

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 = 0.242464559 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + t = 0.242464559 + 0.09375
t = 0.242464559 + 0.09375

Combine like terms: 0.242464559 + 0.09375 = 0.336214559
t = 0.336214559

Simplifying
t = 0.336214559

Subproblem 2
t + -0.09375 = -0.242464559

Simplifying
t + -0.09375 = -0.242464559

Reorder the terms:
-0.09375 + t = -0.242464559

Solving
-0.09375 + t = -0.242464559

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 = -0.242464559 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + t = -0.242464559 + 0.09375
t = -0.242464559 + 0.09375

Combine like terms: -0.242464559 + 0.09375 = -0.148714559
t = -0.148714559

Simplifying
t = -0.148714559

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.336214559, -0.148714559}