5t^2-10t-20=0

Solution for 5t^2-10t-20=0 equation:

Simplifying
5t2 + -10t + -20 = 0

Reorder the terms:
-20 + -10t + 5t2 = 0

Solving
-20 + -10t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + -2t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + -2t + t2)' equal to zero and attempt to solve:

Simplifying
-4 + -2t + t2 = 0

Solving
-4 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + -2t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2t + t2 = 0 + 4
-2t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2t + t2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2t + t2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2t + t2 = 5

Factor a perfect square on the left side:
(t + -1)(t + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(t + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
t + -1 = 2.236067978

Simplifying
t + -1 = 2.236067978

Reorder the terms:
-1 + t = 2.236067978

Solving
-1 + t = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.236067978 + 1
t = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
t = 3.236067978

Simplifying
t = 3.236067978

Subproblem 2
t + -1 = -2.236067978

Simplifying
t + -1 = -2.236067978

Reorder the terms:
-1 + t = -2.236067978

Solving
-1 + t = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.236067978 + 1
t = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
t = -1.236067978

Simplifying
t = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.236067978, -1.236067978}
Solution
t = {3.236067978, -1.236067978}