0=5t^2+20t+3

Solution for 0=5t^2+20t+3 equation:

Simplifying
0 = 5t2 + 20t + 3

Reorder the terms:
0 = 3 + 20t + 5t2

Solving
0 = 3 + 20t + 5t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -20t + -5t2 = 3 + 20t + 5t2 + -3 + -20t + -5t2

Reorder the terms:
-3 + -20t + -5t2 = 3 + -3 + 20t + -20t + 5t2 + -5t2

Combine like terms: 3 + -3 = 0
-3 + -20t + -5t2 = 0 + 20t + -20t + 5t2 + -5t2
-3 + -20t + -5t2 = 20t + -20t + 5t2 + -5t2

Combine like terms: 20t + -20t = 0
-3 + -20t + -5t2 = 0 + 5t2 + -5t2
-3 + -20t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-3 + -20t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 20t + 5t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 20t + 5t2)' equal to zero and attempt to solve:

Simplifying
3 + 20t + 5t2 = 0

Solving
3 + 20t + 5t2 = 0

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

Divide each side by '5'.
0.6 + 4t + t2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 4t + -0.6 + t2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 4t + t2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 4t + t2 = 0 + -0.6
4t + t2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
4t + t2 = -0.6

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = -0.6 + 4

Reorder the terms:
4 + 4t + t2 = -0.6 + 4

Combine like terms: -0.6 + 4 = 3.4
4 + 4t + t2 = 3.4

Factor a perfect square on the left side:
(t + 2)(t + 2) = 3.4

Calculate the square root of the right side: 1.843908891

Break this problem into two subproblems by setting 
(t + 2) equal to 1.843908891 and -1.843908891.

Subproblem 1
t + 2 = 1.843908891

Simplifying
t + 2 = 1.843908891

Reorder the terms:
2 + t = 1.843908891

Solving
2 + t = 1.843908891

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 1.843908891 + -2

Combine like terms: 2 + -2 = 0
0 + t = 1.843908891 + -2
t = 1.843908891 + -2

Combine like terms: 1.843908891 + -2 = -0.156091109
t = -0.156091109

Simplifying
t = -0.156091109

Subproblem 2
t + 2 = -1.843908891

Simplifying
t + 2 = -1.843908891

Reorder the terms:
2 + t = -1.843908891

Solving
2 + t = -1.843908891

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -1.843908891 + -2

Combine like terms: 2 + -2 = 0
0 + t = -1.843908891 + -2
t = -1.843908891 + -2

Combine like terms: -1.843908891 + -2 = -3.843908891
t = -3.843908891

Simplifying
t = -3.843908891

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.156091109, -3.843908891}
Solution
t = {-0.156091109, -3.843908891}