4.905t^2-124.36t-120=0

Solution for 4.905t^2-124.36t-120=0 equation:

Simplifying
4.905t2 + -124.36t + -120 = 0

Reorder the terms:
-120 + -124.36t + 4.905t2 = 0

Solving
-120 + -124.36t + 4.905t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
4.905 the coefficient of the squared term: 

Divide each side by '4.905'.
-24.4648318 + -25.35372069t + t2 = 0

Move the constant term to the right:

Add '24.4648318' to each side of the equation.
-24.4648318 + -25.35372069t + 24.4648318 + t2 = 0 + 24.4648318

Reorder the terms:
-24.4648318 + 24.4648318 + -25.35372069t + t2 = 0 + 24.4648318

Combine like terms: -24.4648318 + 24.4648318 = 0.0000000
0.0000000 + -25.35372069t + t2 = 0 + 24.4648318
-25.35372069t + t2 = 0 + 24.4648318

Combine like terms: 0 + 24.4648318 = 24.4648318
-25.35372069t + t2 = 24.4648318

The t term is -25.35372069t.  Take half its coefficient (-12.67686035).
Square it (160.7027883) and add it to both sides.

Add '160.7027883' to each side of the equation.
-25.35372069t + 160.7027883 + t2 = 24.4648318 + 160.7027883

Reorder the terms:
160.7027883 + -25.35372069t + t2 = 24.4648318 + 160.7027883

Combine like terms: 24.4648318 + 160.7027883 = 185.1676201
160.7027883 + -25.35372069t + t2 = 185.1676201

Factor a perfect square on the left side:
(t + -12.67686035)(t + -12.67686035) = 185.1676201

Calculate the square root of the right side: 13.607630951

Break this problem into two subproblems by setting 
(t + -12.67686035) equal to 13.607630951 and -13.607630951.

Subproblem 1
t + -12.67686035 = 13.607630951

Simplifying
t + -12.67686035 = 13.607630951

Reorder the terms:
-12.67686035 + t = 13.607630951

Solving
-12.67686035 + t = 13.607630951

Solving for variable 't'.

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

Add '12.67686035' to each side of the equation.
-12.67686035 + 12.67686035 + t = 13.607630951 + 12.67686035

Combine like terms: -12.67686035 + 12.67686035 = 0.00000000
0.00000000 + t = 13.607630951 + 12.67686035
t = 13.607630951 + 12.67686035

Combine like terms: 13.607630951 + 12.67686035 = 26.284491301
t = 26.284491301

Simplifying
t = 26.284491301

Subproblem 2
t + -12.67686035 = -13.607630951

Simplifying
t + -12.67686035 = -13.607630951

Reorder the terms:
-12.67686035 + t = -13.607630951

Solving
-12.67686035 + t = -13.607630951

Solving for variable 't'.

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

Add '12.67686035' to each side of the equation.
-12.67686035 + 12.67686035 + t = -13.607630951 + 12.67686035

Combine like terms: -12.67686035 + 12.67686035 = 0.00000000
0.00000000 + t = -13.607630951 + 12.67686035
t = -13.607630951 + 12.67686035

Combine like terms: -13.607630951 + 12.67686035 = -0.930770601
t = -0.930770601

Simplifying
t = -0.930770601

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {26.284491301, -0.930770601}