4.9t^2-6t-17=0

Solution for 4.9t^2-6t-17=0 equation:

Simplifying
4.9t2 + -6t + -17 = 0

Reorder the terms:
-17 + -6t + 4.9t2 = 0

Solving
-17 + -6t + 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'.
-3.469387755 + -1.224489796t + t2 = 0

Move the constant term to the right:

Add '3.469387755' to each side of the equation.
-3.469387755 + -1.224489796t + 3.469387755 + t2 = 0 + 3.469387755

Reorder the terms:
-3.469387755 + 3.469387755 + -1.224489796t + t2 = 0 + 3.469387755

Combine like terms: -3.469387755 + 3.469387755 = 0.000000000
0.000000000 + -1.224489796t + t2 = 0 + 3.469387755
-1.224489796t + t2 = 0 + 3.469387755

Combine like terms: 0 + 3.469387755 = 3.469387755
-1.224489796t + t2 = 3.469387755

The t term is -1.224489796t.  Take half its coefficient (-0.612244898).
Square it (0.3748438151) and add it to both sides.

Add '0.3748438151' to each side of the equation.
-1.224489796t + 0.3748438151 + t2 = 3.469387755 + 0.3748438151

Reorder the terms:
0.3748438151 + -1.224489796t + t2 = 3.469387755 + 0.3748438151

Combine like terms: 3.469387755 + 0.3748438151 = 3.8442315701
0.3748438151 + -1.224489796t + t2 = 3.8442315701

Factor a perfect square on the left side:
(t + -0.612244898)(t + -0.612244898) = 3.8442315701

Calculate the square root of the right side: 1.960671204

Break this problem into two subproblems by setting 
(t + -0.612244898) equal to 1.960671204 and -1.960671204.

Subproblem 1
t + -0.612244898 = 1.960671204

Simplifying
t + -0.612244898 = 1.960671204

Reorder the terms:
-0.612244898 + t = 1.960671204

Solving
-0.612244898 + t = 1.960671204

Solving for variable 't'.

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

Add '0.612244898' to each side of the equation.
-0.612244898 + 0.612244898 + t = 1.960671204 + 0.612244898

Combine like terms: -0.612244898 + 0.612244898 = 0.000000000
0.000000000 + t = 1.960671204 + 0.612244898
t = 1.960671204 + 0.612244898

Combine like terms: 1.960671204 + 0.612244898 = 2.572916102
t = 2.572916102

Simplifying
t = 2.572916102

Subproblem 2
t + -0.612244898 = -1.960671204

Simplifying
t + -0.612244898 = -1.960671204

Reorder the terms:
-0.612244898 + t = -1.960671204

Solving
-0.612244898 + t = -1.960671204

Solving for variable 't'.

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

Add '0.612244898' to each side of the equation.
-0.612244898 + 0.612244898 + t = -1.960671204 + 0.612244898

Combine like terms: -0.612244898 + 0.612244898 = 0.000000000
0.000000000 + t = -1.960671204 + 0.612244898
t = -1.960671204 + 0.612244898

Combine like terms: -1.960671204 + 0.612244898 = -1.348426306
t = -1.348426306

Simplifying
t = -1.348426306

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.572916102, -1.348426306}