4.8t^2+50t-20=0

Solution for 4.8t^2+50t-20=0 equation:

Simplifying
4.8t2 + 50t + -20 = 0

Reorder the terms:
-20 + 50t + 4.8t2 = 0

Solving
-20 + 50t + 4.8t2 = 0

Solving for variable 't'.

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

Divide each side by '4.8'.
-4.166666667 + 10.41666667t + t2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 10.41666667t + 4.166666667 + t2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 10.41666667t + t2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 10.41666667t + t2 = 0 + 4.166666667
10.41666667t + t2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
10.41666667t + t2 = 4.166666667

The t term is 10.41666667t.  Take half its coefficient (5.208333335).
Square it (27.12673613) and add it to both sides.

Add '27.12673613' to each side of the equation.
10.41666667t + 27.12673613 + t2 = 4.166666667 + 27.12673613

Reorder the terms:
27.12673613 + 10.41666667t + t2 = 4.166666667 + 27.12673613

Combine like terms: 4.166666667 + 27.12673613 = 31.293402797
27.12673613 + 10.41666667t + t2 = 31.293402797

Factor a perfect square on the left side:
(t + 5.208333335)(t + 5.208333335) = 31.293402797

Calculate the square root of the right side: 5.594050661

Break this problem into two subproblems by setting 
(t + 5.208333335) equal to 5.594050661 and -5.594050661.

Subproblem 1
t + 5.208333335 = 5.594050661

Simplifying
t + 5.208333335 = 5.594050661

Reorder the terms:
5.208333335 + t = 5.594050661

Solving
5.208333335 + t = 5.594050661

Solving for variable 't'.

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

Add '-5.208333335' to each side of the equation.
5.208333335 + -5.208333335 + t = 5.594050661 + -5.208333335

Combine like terms: 5.208333335 + -5.208333335 = 0.000000000
0.000000000 + t = 5.594050661 + -5.208333335
t = 5.594050661 + -5.208333335

Combine like terms: 5.594050661 + -5.208333335 = 0.385717326
t = 0.385717326

Simplifying
t = 0.385717326

Subproblem 2
t + 5.208333335 = -5.594050661

Simplifying
t + 5.208333335 = -5.594050661

Reorder the terms:
5.208333335 + t = -5.594050661

Solving
5.208333335 + t = -5.594050661

Solving for variable 't'.

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

Add '-5.208333335' to each side of the equation.
5.208333335 + -5.208333335 + t = -5.594050661 + -5.208333335

Combine like terms: 5.208333335 + -5.208333335 = 0.000000000
0.000000000 + t = -5.594050661 + -5.208333335
t = -5.594050661 + -5.208333335

Combine like terms: -5.594050661 + -5.208333335 = -10.802383996
t = -10.802383996

Simplifying
t = -10.802383996

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.385717326, -10.802383996}