0=3+15t-5t^2

Solution for 0=3+15t-5t^2 equation:

Simplifying
0 = 3 + 15t + -5t2

Solving
0 = 3 + 15t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -15t + 5t2 = 3 + 15t + -5t2 + -3 + -15t + 5t2

Reorder the terms:
-3 + -15t + 5t2 = 3 + -3 + 15t + -15t + -5t2 + 5t2

Combine like terms: 3 + -3 = 0
-3 + -15t + 5t2 = 0 + 15t + -15t + -5t2 + 5t2
-3 + -15t + 5t2 = 15t + -15t + -5t2 + 5t2

Combine like terms: 15t + -15t = 0
-3 + -15t + 5t2 = 0 + -5t2 + 5t2
-3 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-3 + -15t + 5t2 = 0

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

Divide each side by '5'.
-0.6 + -3t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -3t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -3t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -3t + t2 = 0 + 0.6
-3t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-3t + t2 = 0.6

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 0.6 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 0.6 + 2.25

Combine like terms: 0.6 + 2.25 = 2.85
2.25 + -3t + t2 = 2.85

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 2.85

Calculate the square root of the right side: 1.688194302

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.688194302 and -1.688194302.

Subproblem 1
t + -1.5 = 1.688194302

Simplifying
t + -1.5 = 1.688194302

Reorder the terms:
-1.5 + t = 1.688194302

Solving
-1.5 + t = 1.688194302

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.688194302 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.688194302 + 1.5
t = 1.688194302 + 1.5

Combine like terms: 1.688194302 + 1.5 = 3.188194302
t = 3.188194302

Simplifying
t = 3.188194302

Subproblem 2
t + -1.5 = -1.688194302

Simplifying
t + -1.5 = -1.688194302

Reorder the terms:
-1.5 + t = -1.688194302

Solving
-1.5 + t = -1.688194302

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.688194302 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.688194302 + 1.5
t = -1.688194302 + 1.5

Combine like terms: -1.688194302 + 1.5 = -0.188194302
t = -0.188194302

Simplifying
t = -0.188194302

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.188194302, -0.188194302}