-16t^2+15t+8=0

Solution for -16t^2+15t+8=0 equation:

Simplifying
-16t2 + 15t + 8 = 0

Reorder the terms:
8 + 15t + -16t2 = 0

Solving
8 + 15t + -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'.
-0.5 + -0.9375t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.9375t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.9375t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.9375t + t2 = 0 + 0.5
-0.9375t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.9375t + t2 = 0.5

The t term is -0.9375t.  Take half its coefficient (-0.46875).
Square it (0.2197265625) and add it to both sides.

Add '0.2197265625' to each side of the equation.
-0.9375t + 0.2197265625 + t2 = 0.5 + 0.2197265625

Reorder the terms:
0.2197265625 + -0.9375t + t2 = 0.5 + 0.2197265625

Combine like terms: 0.5 + 0.2197265625 = 0.7197265625
0.2197265625 + -0.9375t + t2 = 0.7197265625

Factor a perfect square on the left side:
(t + -0.46875)(t + -0.46875) = 0.7197265625

Calculate the square root of the right side: 0.848366998

Break this problem into two subproblems by setting 
(t + -0.46875) equal to 0.848366998 and -0.848366998.

Subproblem 1
t + -0.46875 = 0.848366998

Simplifying
t + -0.46875 = 0.848366998

Reorder the terms:
-0.46875 + t = 0.848366998

Solving
-0.46875 + t = 0.848366998

Solving for variable 't'.

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

Add '0.46875' to each side of the equation.
-0.46875 + 0.46875 + t = 0.848366998 + 0.46875

Combine like terms: -0.46875 + 0.46875 = 0.00000
0.00000 + t = 0.848366998 + 0.46875
t = 0.848366998 + 0.46875

Combine like terms: 0.848366998 + 0.46875 = 1.317116998
t = 1.317116998

Simplifying
t = 1.317116998

Subproblem 2
t + -0.46875 = -0.848366998

Simplifying
t + -0.46875 = -0.848366998

Reorder the terms:
-0.46875 + t = -0.848366998

Solving
-0.46875 + t = -0.848366998

Solving for variable 't'.

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

Add '0.46875' to each side of the equation.
-0.46875 + 0.46875 + t = -0.848366998 + 0.46875

Combine like terms: -0.46875 + 0.46875 = 0.00000
0.00000 + t = -0.848366998 + 0.46875
t = -0.848366998 + 0.46875

Combine like terms: -0.848366998 + 0.46875 = -0.379616998
t = -0.379616998

Simplifying
t = -0.379616998

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.317116998, -0.379616998}