0=5t^2-10t-3

Solution for 0=5t^2-10t-3 equation:

Simplifying
0 = 5t2 + -10t + -3

Reorder the terms:
0 = -3 + -10t + 5t2

Solving
0 = -3 + -10t + 5t2

Solving for variable 't'.

Combine like terms: 0 + 3 = 3
3 + 10t + -5t2 = -3 + -10t + 5t2 + 3 + 10t + -5t2

Reorder the terms:
3 + 10t + -5t2 = -3 + 3 + -10t + 10t + 5t2 + -5t2

Combine like terms: -3 + 3 = 0
3 + 10t + -5t2 = 0 + -10t + 10t + 5t2 + -5t2
3 + 10t + -5t2 = -10t + 10t + 5t2 + -5t2

Combine like terms: -10t + 10t = 0
3 + 10t + -5t2 = 0 + 5t2 + -5t2
3 + 10t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
3 + 10t + -5t2 = 0

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

Divide each side by '-5'.
-0.6 + -2t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2t + t2 = 0 + 0.6
-2t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2t + t2 = 0.6

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 0.6 + 1

Reorder the terms:
1 + -2t + t2 = 0.6 + 1

Combine like terms: 0.6 + 1 = 1.6
1 + -2t + t2 = 1.6

Factor a perfect square on the left side:
(t + -1)(t + -1) = 1.6

Calculate the square root of the right side: 1.264911064

Break this problem into two subproblems by setting 
(t + -1) equal to 1.264911064 and -1.264911064.

Subproblem 1
t + -1 = 1.264911064

Simplifying
t + -1 = 1.264911064

Reorder the terms:
-1 + t = 1.264911064

Solving
-1 + t = 1.264911064

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.264911064 + 1
t = 1.264911064 + 1

Combine like terms: 1.264911064 + 1 = 2.264911064
t = 2.264911064

Simplifying
t = 2.264911064

Subproblem 2
t + -1 = -1.264911064

Simplifying
t + -1 = -1.264911064

Reorder the terms:
-1 + t = -1.264911064

Solving
-1 + t = -1.264911064

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.264911064 + 1
t = -1.264911064 + 1

Combine like terms: -1.264911064 + 1 = -0.264911064
t = -0.264911064

Simplifying
t = -0.264911064

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.264911064, -0.264911064}