5=5t^2-16t+3

Solution for 5=5t^2-16t+3 equation:

Simplifying
5 = 5t2 + -16t + 3

Reorder the terms:
5 = 3 + -16t + 5t2

Solving
5 = 3 + -16t + 5t2

Solving for variable 't'.

Combine like terms: 5 + -3 = 2
2 + 16t + -5t2 = 3 + -16t + 5t2 + -3 + 16t + -5t2

Reorder the terms:
2 + 16t + -5t2 = 3 + -3 + -16t + 16t + 5t2 + -5t2

Combine like terms: 3 + -3 = 0
2 + 16t + -5t2 = 0 + -16t + 16t + 5t2 + -5t2
2 + 16t + -5t2 = -16t + 16t + 5t2 + -5t2

Combine like terms: -16t + 16t = 0
2 + 16t + -5t2 = 0 + 5t2 + -5t2
2 + 16t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
2 + 16t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.4 + -3.2t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -3.2t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -3.2t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -3.2t + t2 = 0 + 0.4
-3.2t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-3.2t + t2 = 0.4

The t term is -3.2t.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2t + 2.56 + t2 = 0.4 + 2.56

Reorder the terms:
2.56 + -3.2t + t2 = 0.4 + 2.56

Combine like terms: 0.4 + 2.56 = 2.96
2.56 + -3.2t + t2 = 2.96

Factor a perfect square on the left side:
(t + -1.6)(t + -1.6) = 2.96

Calculate the square root of the right side: 1.720465053

Break this problem into two subproblems by setting 
(t + -1.6) equal to 1.720465053 and -1.720465053.

Subproblem 1
t + -1.6 = 1.720465053

Simplifying
t + -1.6 = 1.720465053

Reorder the terms:
-1.6 + t = 1.720465053

Solving
-1.6 + t = 1.720465053

Solving for variable 't'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + t = 1.720465053 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + t = 1.720465053 + 1.6
t = 1.720465053 + 1.6

Combine like terms: 1.720465053 + 1.6 = 3.320465053
t = 3.320465053

Simplifying
t = 3.320465053

Subproblem 2
t + -1.6 = -1.720465053

Simplifying
t + -1.6 = -1.720465053

Reorder the terms:
-1.6 + t = -1.720465053

Solving
-1.6 + t = -1.720465053

Solving for variable 't'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + t = -1.720465053 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + t = -1.720465053 + 1.6
t = -1.720465053 + 1.6

Combine like terms: -1.720465053 + 1.6 = -0.120465053
t = -0.120465053

Simplifying
t = -0.120465053

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.320465053, -0.120465053}