4.9t^2-245t+1960=0

Solution for 4.9t^2-245t+1960=0 equation:

Simplifying
4.9t2 + -245t + 1960 = 0

Reorder the terms:
1960 + -245t + 4.9t2 = 0

Solving
1960 + -245t + 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'.
400 + -50t + t2 = 0

Move the constant term to the right:

Add '-400' to each side of the equation.
400 + -50t + -400 + t2 = 0 + -400

Reorder the terms:
400 + -400 + -50t + t2 = 0 + -400

Combine like terms: 400 + -400 = 0
0 + -50t + t2 = 0 + -400
-50t + t2 = 0 + -400

Combine like terms: 0 + -400 = -400
-50t + t2 = -400

The t term is -50t.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50t + 625 + t2 = -400 + 625

Reorder the terms:
625 + -50t + t2 = -400 + 625

Combine like terms: -400 + 625 = 225
625 + -50t + t2 = 225

Factor a perfect square on the left side:
(t + -25)(t + -25) = 225

Calculate the square root of the right side: 15

Break this problem into two subproblems by setting 
(t + -25) equal to 15 and -15.

Subproblem 1
t + -25 = 15

Simplifying
t + -25 = 15

Reorder the terms:
-25 + t = 15

Solving
-25 + t = 15

Solving for variable 't'.

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

Add '25' to each side of the equation.
-25 + 25 + t = 15 + 25

Combine like terms: -25 + 25 = 0
0 + t = 15 + 25
t = 15 + 25

Combine like terms: 15 + 25 = 40
t = 40

Simplifying
t = 40

Subproblem 2
t + -25 = -15

Simplifying
t + -25 = -15

Reorder the terms:
-25 + t = -15

Solving
-25 + t = -15

Solving for variable 't'.

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

Add '25' to each side of the equation.
-25 + 25 + t = -15 + 25

Combine like terms: -25 + 25 = 0
0 + t = -15 + 25
t = -15 + 25

Combine like terms: -15 + 25 = 10
t = 10

Simplifying
t = 10

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {40, 10}