0=8t^2+16t-103

Solution for 0=8t^2+16t-103 equation:

Simplifying
0 = 8t2 + 16t + -103

Reorder the terms:
0 = -103 + 16t + 8t2

Solving
0 = -103 + 16t + 8t2

Solving for variable 't'.

Combine like terms: 0 + 103 = 103
103 + -16t + -8t2 = -103 + 16t + 8t2 + 103 + -16t + -8t2

Reorder the terms:
103 + -16t + -8t2 = -103 + 103 + 16t + -16t + 8t2 + -8t2

Combine like terms: -103 + 103 = 0
103 + -16t + -8t2 = 0 + 16t + -16t + 8t2 + -8t2
103 + -16t + -8t2 = 16t + -16t + 8t2 + -8t2

Combine like terms: 16t + -16t = 0
103 + -16t + -8t2 = 0 + 8t2 + -8t2
103 + -16t + -8t2 = 8t2 + -8t2

Combine like terms: 8t2 + -8t2 = 0
103 + -16t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-12.875 + 2t + t2 = 0

Move the constant term to the right:

Add '12.875' to each side of the equation.
-12.875 + 2t + 12.875 + t2 = 0 + 12.875

Reorder the terms:
-12.875 + 12.875 + 2t + t2 = 0 + 12.875

Combine like terms: -12.875 + 12.875 = 0.000
0.000 + 2t + t2 = 0 + 12.875
2t + t2 = 0 + 12.875

Combine like terms: 0 + 12.875 = 12.875
2t + t2 = 12.875

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 12.875 + 1

Reorder the terms:
1 + 2t + t2 = 12.875 + 1

Combine like terms: 12.875 + 1 = 13.875
1 + 2t + t2 = 13.875

Factor a perfect square on the left side:
(t + 1)(t + 1) = 13.875

Calculate the square root of the right side: 3.724916106

Break this problem into two subproblems by setting 
(t + 1) equal to 3.724916106 and -3.724916106.

Subproblem 1
t + 1 = 3.724916106

Simplifying
t + 1 = 3.724916106

Reorder the terms:
1 + t = 3.724916106

Solving
1 + t = 3.724916106

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 3.724916106 + -1

Combine like terms: 1 + -1 = 0
0 + t = 3.724916106 + -1
t = 3.724916106 + -1

Combine like terms: 3.724916106 + -1 = 2.724916106
t = 2.724916106

Simplifying
t = 2.724916106

Subproblem 2
t + 1 = -3.724916106

Simplifying
t + 1 = -3.724916106

Reorder the terms:
1 + t = -3.724916106

Solving
1 + t = -3.724916106

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -3.724916106 + -1

Combine like terms: 1 + -1 = 0
0 + t = -3.724916106 + -1
t = -3.724916106 + -1

Combine like terms: -3.724916106 + -1 = -4.724916106
t = -4.724916106

Simplifying
t = -4.724916106

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.724916106, -4.724916106}