-16t^2+39.2t-15.6=0

Solution for -16t^2+39.2t-15.6=0 equation:

Simplifying
-16t2 + 39.2t + -15.6 = 0

Reorder the terms:
-15.6 + 39.2t + -16t2 = 0

Solving
-15.6 + 39.2t + -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'.
0.975 + -2.45t + t2 = 0

Move the constant term to the right:

Add '-0.975' to each side of the equation.
0.975 + -2.45t + -0.975 + t2 = 0 + -0.975

Reorder the terms:
0.975 + -0.975 + -2.45t + t2 = 0 + -0.975

Combine like terms: 0.975 + -0.975 = 0.000
0.000 + -2.45t + t2 = 0 + -0.975
-2.45t + t2 = 0 + -0.975

Combine like terms: 0 + -0.975 = -0.975
-2.45t + t2 = -0.975

The t term is -2.45t.  Take half its coefficient (-1.225).
Square it (1.500625) and add it to both sides.

Add '1.500625' to each side of the equation.
-2.45t + 1.500625 + t2 = -0.975 + 1.500625

Reorder the terms:
1.500625 + -2.45t + t2 = -0.975 + 1.500625

Combine like terms: -0.975 + 1.500625 = 0.525625
1.500625 + -2.45t + t2 = 0.525625

Factor a perfect square on the left side:
(t + -1.225)(t + -1.225) = 0.525625

Calculate the square root of the right side: 0.725

Break this problem into two subproblems by setting 
(t + -1.225) equal to 0.725 and -0.725.

Subproblem 1
t + -1.225 = 0.725

Simplifying
t + -1.225 = 0.725

Reorder the terms:
-1.225 + t = 0.725

Solving
-1.225 + t = 0.725

Solving for variable 't'.

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

Add '1.225' to each side of the equation.
-1.225 + 1.225 + t = 0.725 + 1.225

Combine like terms: -1.225 + 1.225 = 0.000
0.000 + t = 0.725 + 1.225
t = 0.725 + 1.225

Combine like terms: 0.725 + 1.225 = 1.95
t = 1.95

Simplifying
t = 1.95

Subproblem 2
t + -1.225 = -0.725

Simplifying
t + -1.225 = -0.725

Reorder the terms:
-1.225 + t = -0.725

Solving
-1.225 + t = -0.725

Solving for variable 't'.

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

Add '1.225' to each side of the equation.
-1.225 + 1.225 + t = -0.725 + 1.225

Combine like terms: -1.225 + 1.225 = 0.000
0.000 + t = -0.725 + 1.225
t = -0.725 + 1.225

Combine like terms: -0.725 + 1.225 = 0.5
t = 0.5

Simplifying
t = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.95, 0.5}