5t^2-8t-3=0

Solution for 5t^2-8t-3=0 equation:

Simplifying
5t2 + -8t + -3 = 0

Reorder the terms:
-3 + -8t + 5t2 = 0

Solving
-3 + -8t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-0.6 + -1.6t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.6t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.6t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.6t + t2 = 0 + 0.6
-1.6t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.6t + t2 = 0.6

The t term is -1.6t.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6t + 0.64 + t2 = 0.6 + 0.64

Reorder the terms:
0.64 + -1.6t + t2 = 0.6 + 0.64

Combine like terms: 0.6 + 0.64 = 1.24
0.64 + -1.6t + t2 = 1.24

Factor a perfect square on the left side:
(t + -0.8)(t + -0.8) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(t + -0.8) equal to 1.113552873 and -1.113552873.

Subproblem 1
t + -0.8 = 1.113552873

Simplifying
t + -0.8 = 1.113552873

Reorder the terms:
-0.8 + t = 1.113552873

Solving
-0.8 + t = 1.113552873

Solving for variable 't'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + t = 1.113552873 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + t = 1.113552873 + 0.8
t = 1.113552873 + 0.8

Combine like terms: 1.113552873 + 0.8 = 1.913552873
t = 1.913552873

Simplifying
t = 1.913552873

Subproblem 2
t + -0.8 = -1.113552873

Simplifying
t + -0.8 = -1.113552873

Reorder the terms:
-0.8 + t = -1.113552873

Solving
-0.8 + t = -1.113552873

Solving for variable 't'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + t = -1.113552873 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + t = -1.113552873 + 0.8
t = -1.113552873 + 0.8

Combine like terms: -1.113552873 + 0.8 = -0.313552873
t = -0.313552873

Simplifying
t = -0.313552873

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.913552873, -0.313552873}