-16t^2+45t+6=5

Solution for -16t^2+45t+6=5 equation:

Simplifying
-16t2 + 45t + 6 = 5

Reorder the terms:
6 + 45t + -16t2 = 5

Solving
6 + 45t + -16t2 = 5

Solving for variable 't'.

Reorder the terms:
6 + -5 + 45t + -16t2 = 5 + -5

Combine like terms: 6 + -5 = 1
1 + 45t + -16t2 = 5 + -5

Combine like terms: 5 + -5 = 0
1 + 45t + -16t2 = 0

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

Divide each side by '-16'.
-0.0625 + -2.8125t + t2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -2.8125t + 0.0625 + t2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -2.8125t + t2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -2.8125t + t2 = 0 + 0.0625
-2.8125t + t2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-2.8125t + t2 = 0.0625

The t term is -2.8125t.  Take half its coefficient (-1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
-2.8125t + 1.977539063 + t2 = 0.0625 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125t + t2 = 0.0625 + 1.977539063

Combine like terms: 0.0625 + 1.977539063 = 2.040039063
1.977539063 + -2.8125t + t2 = 2.040039063

Factor a perfect square on the left side:
(t + -1.40625)(t + -1.40625) = 2.040039063

Calculate the square root of the right side: 1.42829936

Break this problem into two subproblems by setting 
(t + -1.40625) equal to 1.42829936 and -1.42829936.

Subproblem 1
t + -1.40625 = 1.42829936

Simplifying
t + -1.40625 = 1.42829936

Reorder the terms:
-1.40625 + t = 1.42829936

Solving
-1.40625 + t = 1.42829936

Solving for variable 't'.

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

Add '1.40625' to each side of the equation.
-1.40625 + 1.40625 + t = 1.42829936 + 1.40625

Combine like terms: -1.40625 + 1.40625 = 0.00000
0.00000 + t = 1.42829936 + 1.40625
t = 1.42829936 + 1.40625

Combine like terms: 1.42829936 + 1.40625 = 2.83454936
t = 2.83454936

Simplifying
t = 2.83454936

Subproblem 2
t + -1.40625 = -1.42829936

Simplifying
t + -1.40625 = -1.42829936

Reorder the terms:
-1.40625 + t = -1.42829936

Solving
-1.40625 + t = -1.42829936

Solving for variable 't'.

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

Add '1.40625' to each side of the equation.
-1.40625 + 1.40625 + t = -1.42829936 + 1.40625

Combine like terms: -1.40625 + 1.40625 = 0.00000
0.00000 + t = -1.42829936 + 1.40625
t = -1.42829936 + 1.40625

Combine like terms: -1.42829936 + 1.40625 = -0.02204936
t = -0.02204936

Simplifying
t = -0.02204936

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.83454936, -0.02204936}