5=3+5t+2t^2

Solution for 5=3+5t+2t^2 equation:

Simplifying
5 = 3 + 5t + 2t2

Solving
5 = 3 + 5t + 2t2

Solving for variable 't'.

Combine like terms: 5 + -3 = 2
2 + -5t + -2t2 = 3 + 5t + 2t2 + -3 + -5t + -2t2

Reorder the terms:
2 + -5t + -2t2 = 3 + -3 + 5t + -5t + 2t2 + -2t2

Combine like terms: 3 + -3 = 0
2 + -5t + -2t2 = 0 + 5t + -5t + 2t2 + -2t2
2 + -5t + -2t2 = 5t + -5t + 2t2 + -2t2

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

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

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

Divide each side by '-2'.
-1 + 2.5t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.5t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.5t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.5t + t2 = 0 + 1
2.5t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.5t + t2 = 1

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = 1 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + 2.5t + t2 = 2.5625

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(t + 1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
t + 1.25 = 1.600781059

Simplifying
t + 1.25 = 1.600781059

Reorder the terms:
1.25 + t = 1.600781059

Solving
1.25 + t = 1.600781059

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = 1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 1.600781059 + -1.25
t = 1.600781059 + -1.25

Combine like terms: 1.600781059 + -1.25 = 0.350781059
t = 0.350781059

Simplifying
t = 0.350781059

Subproblem 2
t + 1.25 = -1.600781059

Simplifying
t + 1.25 = -1.600781059

Reorder the terms:
1.25 + t = -1.600781059

Solving
1.25 + t = -1.600781059

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = -1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -1.600781059 + -1.25
t = -1.600781059 + -1.25

Combine like terms: -1.600781059 + -1.25 = -2.850781059
t = -2.850781059

Simplifying
t = -2.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.350781059, -2.850781059}