-4.9t^2+29.4t-24.5=0

Solution for -4.9t^2+29.4t-24.5=0 equation:

Simplifying
-4.9t2 + 29.4t + -24.5 = 0

Reorder the terms:
-24.5 + 29.4t + -4.9t2 = 0

Solving
-24.5 + 29.4t + -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'.
5 + -6t + t2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -6t + -5 + t2 = 0 + -5

Reorder the terms:
5 + -5 + -6t + t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6t + t2 = 0 + -5
-6t + t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6t + t2 = -5

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -5 + 9

Reorder the terms:
9 + -6t + t2 = -5 + 9

Combine like terms: -5 + 9 = 4
9 + -6t + t2 = 4

Factor a perfect square on the left side:
(t + -3)(t + -3) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(t + -3) equal to 2 and -2.

Subproblem 1
t + -3 = 2

Simplifying
t + -3 = 2

Reorder the terms:
-3 + t = 2

Solving
-3 + t = 2

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 2 + 3

Combine like terms: -3 + 3 = 0
0 + t = 2 + 3
t = 2 + 3

Combine like terms: 2 + 3 = 5
t = 5

Simplifying
t = 5

Subproblem 2
t + -3 = -2

Simplifying
t + -3 = -2

Reorder the terms:
-3 + t = -2

Solving
-3 + t = -2

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -2 + 3

Combine like terms: -3 + 3 = 0
0 + t = -2 + 3
t = -2 + 3

Combine like terms: -2 + 3 = 1
t = 1

Simplifying
t = 1

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5, 1}