4.905t^2-18t-50=0

Solution for 4.905t^2-18t-50=0 equation:

Simplifying
4.905t2 + -18t + -50 = 0

Reorder the terms:
-50 + -18t + 4.905t2 = 0

Solving
-50 + -18t + 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'.
-10.19367992 + -3.669724771t + t2 = 0

Move the constant term to the right:

Add '10.19367992' to each side of the equation.
-10.19367992 + -3.669724771t + 10.19367992 + t2 = 0 + 10.19367992

Reorder the terms:
-10.19367992 + 10.19367992 + -3.669724771t + t2 = 0 + 10.19367992

Combine like terms: -10.19367992 + 10.19367992 = 0.00000000
0.00000000 + -3.669724771t + t2 = 0 + 10.19367992
-3.669724771t + t2 = 0 + 10.19367992

Combine like terms: 0 + 10.19367992 = 10.19367992
-3.669724771t + t2 = 10.19367992

The t term is -3.669724771t.  Take half its coefficient (-1.834862386).
Square it (3.366719976) and add it to both sides.

Add '3.366719976' to each side of the equation.
-3.669724771t + 3.366719976 + t2 = 10.19367992 + 3.366719976

Reorder the terms:
3.366719976 + -3.669724771t + t2 = 10.19367992 + 3.366719976

Combine like terms: 10.19367992 + 3.366719976 = 13.560399896
3.366719976 + -3.669724771t + t2 = 13.560399896

Factor a perfect square on the left side:
(t + -1.834862386)(t + -1.834862386) = 13.560399896

Calculate the square root of the right side: 3.682444826

Break this problem into two subproblems by setting 
(t + -1.834862386) equal to 3.682444826 and -3.682444826.

Subproblem 1
t + -1.834862386 = 3.682444826

Simplifying
t + -1.834862386 = 3.682444826

Reorder the terms:
-1.834862386 + t = 3.682444826

Solving
-1.834862386 + t = 3.682444826

Solving for variable 't'.

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

Add '1.834862386' to each side of the equation.
-1.834862386 + 1.834862386 + t = 3.682444826 + 1.834862386

Combine like terms: -1.834862386 + 1.834862386 = 0.000000000
0.000000000 + t = 3.682444826 + 1.834862386
t = 3.682444826 + 1.834862386

Combine like terms: 3.682444826 + 1.834862386 = 5.517307212
t = 5.517307212

Simplifying
t = 5.517307212

Subproblem 2
t + -1.834862386 = -3.682444826

Simplifying
t + -1.834862386 = -3.682444826

Reorder the terms:
-1.834862386 + t = -3.682444826

Solving
-1.834862386 + t = -3.682444826

Solving for variable 't'.

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

Add '1.834862386' to each side of the equation.
-1.834862386 + 1.834862386 + t = -3.682444826 + 1.834862386

Combine like terms: -1.834862386 + 1.834862386 = 0.000000000
0.000000000 + t = -3.682444826 + 1.834862386
t = -3.682444826 + 1.834862386

Combine like terms: -3.682444826 + 1.834862386 = -1.84758244
t = -1.84758244

Simplifying
t = -1.84758244

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.517307212, -1.84758244}