8t=5+2t^2

Solution for 8t=5+2t^2 equation:

Simplifying
8t = 5 + 2t2

Solving
8t = 5 + 2t2

Solving for variable 't'.

Reorder the terms:
-5 + 8t + -2t2 = 5 + 2t2 + -5 + -2t2

Reorder the terms:
-5 + 8t + -2t2 = 5 + -5 + 2t2 + -2t2

Combine like terms: 5 + -5 = 0
-5 + 8t + -2t2 = 0 + 2t2 + -2t2
-5 + 8t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
-5 + 8t + -2t2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2.5 + -4t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4t + t2 = 0 + -2.5
-4t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4t + t2 = -2.5

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -2.5 + 4

Reorder the terms:
4 + -4t + t2 = -2.5 + 4

Combine like terms: -2.5 + 4 = 1.5
4 + -4t + t2 = 1.5

Factor a perfect square on the left side:
(t + -2)(t + -2) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(t + -2) equal to 1.224744871 and -1.224744871.

Subproblem 1
t + -2 = 1.224744871

Simplifying
t + -2 = 1.224744871

Reorder the terms:
-2 + t = 1.224744871

Solving
-2 + t = 1.224744871

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 1.224744871 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1.224744871 + 2
t = 1.224744871 + 2

Combine like terms: 1.224744871 + 2 = 3.224744871
t = 3.224744871

Simplifying
t = 3.224744871

Subproblem 2
t + -2 = -1.224744871

Simplifying
t + -2 = -1.224744871

Reorder the terms:
-2 + t = -1.224744871

Solving
-2 + t = -1.224744871

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -1.224744871 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1.224744871 + 2
t = -1.224744871 + 2

Combine like terms: -1.224744871 + 2 = 0.775255129
t = 0.775255129

Simplifying
t = 0.775255129

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.224744871, 0.775255129}