4.9t^2-15t-20=0

Solution for 4.9t^2-15t-20=0 equation:

Simplifying
4.9t2 + -15t + -20 = 0

Reorder the terms:
-20 + -15t + 4.9t2 = 0

Solving
-20 + -15t + 4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '4.9'.
-4.081632653 + -3.06122449t + t2 = 0

Move the constant term to the right:

Add '4.081632653' to each side of the equation.
-4.081632653 + -3.06122449t + 4.081632653 + t2 = 0 + 4.081632653

Reorder the terms:
-4.081632653 + 4.081632653 + -3.06122449t + t2 = 0 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + -3.06122449t + t2 = 0 + 4.081632653
-3.06122449t + t2 = 0 + 4.081632653

Combine like terms: 0 + 4.081632653 = 4.081632653
-3.06122449t + t2 = 4.081632653

The t term is -3.06122449t.  Take half its coefficient (-1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
-3.06122449t + 2.342773845 + t2 = 4.081632653 + 2.342773845

Reorder the terms:
2.342773845 + -3.06122449t + t2 = 4.081632653 + 2.342773845

Combine like terms: 4.081632653 + 2.342773845 = 6.424406498
2.342773845 + -3.06122449t + t2 = 6.424406498

Factor a perfect square on the left side:
(t + -1.530612245)(t + -1.530612245) = 6.424406498

Calculate the square root of the right side: 2.534641296

Break this problem into two subproblems by setting 
(t + -1.530612245) equal to 2.534641296 and -2.534641296.

Subproblem 1
t + -1.530612245 = 2.534641296

Simplifying
t + -1.530612245 = 2.534641296

Reorder the terms:
-1.530612245 + t = 2.534641296

Solving
-1.530612245 + t = 2.534641296

Solving for variable 't'.

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

Add '1.530612245' to each side of the equation.
-1.530612245 + 1.530612245 + t = 2.534641296 + 1.530612245

Combine like terms: -1.530612245 + 1.530612245 = 0.000000000
0.000000000 + t = 2.534641296 + 1.530612245
t = 2.534641296 + 1.530612245

Combine like terms: 2.534641296 + 1.530612245 = 4.065253541
t = 4.065253541

Simplifying
t = 4.065253541

Subproblem 2
t + -1.530612245 = -2.534641296

Simplifying
t + -1.530612245 = -2.534641296

Reorder the terms:
-1.530612245 + t = -2.534641296

Solving
-1.530612245 + t = -2.534641296

Solving for variable 't'.

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

Add '1.530612245' to each side of the equation.
-1.530612245 + 1.530612245 + t = -2.534641296 + 1.530612245

Combine like terms: -1.530612245 + 1.530612245 = 0.000000000
0.000000000 + t = -2.534641296 + 1.530612245
t = -2.534641296 + 1.530612245

Combine like terms: -2.534641296 + 1.530612245 = -1.004029051
t = -1.004029051

Simplifying
t = -1.004029051

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.065253541, -1.004029051}