4.9t^2-13t-8.61=0

Solution for 4.9t^2-13t-8.61=0 equation:

Simplifying
4.9t2 + -13t + -8.61 = 0

Reorder the terms:
-8.61 + -13t + 4.9t2 = 0

Solving
-8.61 + -13t + 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'.
-1.757142857 + -2.653061224t + t2 = 0

Move the constant term to the right:

Add '1.757142857' to each side of the equation.
-1.757142857 + -2.653061224t + 1.757142857 + t2 = 0 + 1.757142857

Reorder the terms:
-1.757142857 + 1.757142857 + -2.653061224t + t2 = 0 + 1.757142857

Combine like terms: -1.757142857 + 1.757142857 = 0.000000000
0.000000000 + -2.653061224t + t2 = 0 + 1.757142857
-2.653061224t + t2 = 0 + 1.757142857

Combine like terms: 0 + 1.757142857 = 1.757142857
-2.653061224t + t2 = 1.757142857

The t term is -2.653061224t.  Take half its coefficient (-1.326530612).
Square it (1.759683465) and add it to both sides.

Add '1.759683465' to each side of the equation.
-2.653061224t + 1.759683465 + t2 = 1.757142857 + 1.759683465

Reorder the terms:
1.759683465 + -2.653061224t + t2 = 1.757142857 + 1.759683465

Combine like terms: 1.757142857 + 1.759683465 = 3.516826322
1.759683465 + -2.653061224t + t2 = 3.516826322

Factor a perfect square on the left side:
(t + -1.326530612)(t + -1.326530612) = 3.516826322

Calculate the square root of the right side: 1.875320325

Break this problem into two subproblems by setting 
(t + -1.326530612) equal to 1.875320325 and -1.875320325.

Subproblem 1
t + -1.326530612 = 1.875320325

Simplifying
t + -1.326530612 = 1.875320325

Reorder the terms:
-1.326530612 + t = 1.875320325

Solving
-1.326530612 + t = 1.875320325

Solving for variable 't'.

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

Add '1.326530612' to each side of the equation.
-1.326530612 + 1.326530612 + t = 1.875320325 + 1.326530612

Combine like terms: -1.326530612 + 1.326530612 = 0.000000000
0.000000000 + t = 1.875320325 + 1.326530612
t = 1.875320325 + 1.326530612

Combine like terms: 1.875320325 + 1.326530612 = 3.201850937
t = 3.201850937

Simplifying
t = 3.201850937

Subproblem 2
t + -1.326530612 = -1.875320325

Simplifying
t + -1.326530612 = -1.875320325

Reorder the terms:
-1.326530612 + t = -1.875320325

Solving
-1.326530612 + t = -1.875320325

Solving for variable 't'.

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

Add '1.326530612' to each side of the equation.
-1.326530612 + 1.326530612 + t = -1.875320325 + 1.326530612

Combine like terms: -1.326530612 + 1.326530612 = 0.000000000
0.000000000 + t = -1.875320325 + 1.326530612
t = -1.875320325 + 1.326530612

Combine like terms: -1.875320325 + 1.326530612 = -0.548789713
t = -0.548789713

Simplifying
t = -0.548789713

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.201850937, -0.548789713}