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 = 0.002540608
1.759683465 + -2.653061224t + t2 = 0.002540608

Factor a perfect square on the left side:
(t + -1.326530612)(t + -1.326530612) = 0.002540608

Calculate the square root of the right side: 0.050404444

Break this problem into two subproblems by setting 
(t + -1.326530612) equal to 0.050404444 and -0.050404444.

Subproblem 1
t + -1.326530612 = 0.050404444

Simplifying
t + -1.326530612 = 0.050404444

Reorder the terms:
-1.326530612 + t = 0.050404444

Solving
-1.326530612 + t = 0.050404444

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 = 0.050404444 + 1.326530612

Combine like terms: -1.326530612 + 1.326530612 = 0.000000000
0.000000000 + t = 0.050404444 + 1.326530612
t = 0.050404444 + 1.326530612

Combine like terms: 0.050404444 + 1.326530612 = 1.376935056
t = 1.376935056

Simplifying
t = 1.376935056

Subproblem 2
t + -1.326530612 = -0.050404444

Simplifying
t + -1.326530612 = -0.050404444

Reorder the terms:
-1.326530612 + t = -0.050404444

Solving
-1.326530612 + t = -0.050404444

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 = -0.050404444 + 1.326530612

Combine like terms: -1.326530612 + 1.326530612 = 0.000000000
0.000000000 + t = -0.050404444 + 1.326530612
t = -0.050404444 + 1.326530612

Combine like terms: -0.050404444 + 1.326530612 = 1.276126168
t = 1.276126168

Simplifying
t = 1.276126168

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.376935056, 1.276126168}