4.9t^2-26t+17.2=0

Solution for 4.9t^2-26t+17.2=0 equation:

Simplifying
4.9t2 + -26t + 17.2 = 0

Reorder the terms:
17.2 + -26t + 4.9t2 = 0

Solving
17.2 + -26t + 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'.
3.510204082 + -5.306122449t + t2 = 0

Move the constant term to the right:

Add '-3.510204082' to each side of the equation.
3.510204082 + -5.306122449t + -3.510204082 + t2 = 0 + -3.510204082

Reorder the terms:
3.510204082 + -3.510204082 + -5.306122449t + t2 = 0 + -3.510204082

Combine like terms: 3.510204082 + -3.510204082 = 0.000000000
0.000000000 + -5.306122449t + t2 = 0 + -3.510204082
-5.306122449t + t2 = 0 + -3.510204082

Combine like terms: 0 + -3.510204082 = -3.510204082
-5.306122449t + t2 = -3.510204082

The t term is -5.306122449t.  Take half its coefficient (-2.653061225).
Square it (7.038733864) and add it to both sides.

Add '7.038733864' to each side of the equation.
-5.306122449t + 7.038733864 + t2 = -3.510204082 + 7.038733864

Reorder the terms:
7.038733864 + -5.306122449t + t2 = -3.510204082 + 7.038733864

Combine like terms: -3.510204082 + 7.038733864 = 3.528529782
7.038733864 + -5.306122449t + t2 = 3.528529782

Factor a perfect square on the left side:
(t + -2.653061225)(t + -2.653061225) = 3.528529782

Calculate the square root of the right side: 1.878438123

Break this problem into two subproblems by setting 
(t + -2.653061225) equal to 1.878438123 and -1.878438123.

Subproblem 1
t + -2.653061225 = 1.878438123

Simplifying
t + -2.653061225 = 1.878438123

Reorder the terms:
-2.653061225 + t = 1.878438123

Solving
-2.653061225 + t = 1.878438123

Solving for variable 't'.

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

Add '2.653061225' to each side of the equation.
-2.653061225 + 2.653061225 + t = 1.878438123 + 2.653061225

Combine like terms: -2.653061225 + 2.653061225 = 0.000000000
0.000000000 + t = 1.878438123 + 2.653061225
t = 1.878438123 + 2.653061225

Combine like terms: 1.878438123 + 2.653061225 = 4.531499348
t = 4.531499348

Simplifying
t = 4.531499348

Subproblem 2
t + -2.653061225 = -1.878438123

Simplifying
t + -2.653061225 = -1.878438123

Reorder the terms:
-2.653061225 + t = -1.878438123

Solving
-2.653061225 + t = -1.878438123

Solving for variable 't'.

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

Add '2.653061225' to each side of the equation.
-2.653061225 + 2.653061225 + t = -1.878438123 + 2.653061225

Combine like terms: -2.653061225 + 2.653061225 = 0.000000000
0.000000000 + t = -1.878438123 + 2.653061225
t = -1.878438123 + 2.653061225

Combine like terms: -1.878438123 + 2.653061225 = 0.774623102
t = 0.774623102

Simplifying
t = 0.774623102

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.531499348, 0.774623102}