-16t^2+120t+50=30

Solution for -16t^2+120t+50=30 equation:

Simplifying
-16t2 + 120t + 50 = 30

Reorder the terms:
50 + 120t + -16t2 = 30

Solving
50 + 120t + -16t2 = 30

Solving for variable 't'.

Reorder the terms:
50 + -30 + 120t + -16t2 = 30 + -30

Combine like terms: 50 + -30 = 20
20 + 120t + -16t2 = 30 + -30

Combine like terms: 30 + -30 = 0
20 + 120t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 30t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + 30t + -4t2)' equal to zero and attempt to solve:

Simplifying
5 + 30t + -4t2 = 0

Solving
5 + 30t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -7.5t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -7.5t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -7.5t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -7.5t + t2 = 0 + 1.25
-7.5t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-7.5t + t2 = 1.25

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = 1.25 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 1.25 + 14.0625

Combine like terms: 1.25 + 14.0625 = 15.3125
14.0625 + -7.5t + t2 = 15.3125

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 15.3125

Calculate the square root of the right side: 3.913118961

Break this problem into two subproblems by setting 
(t + -3.75) equal to 3.913118961 and -3.913118961.

Subproblem 1
t + -3.75 = 3.913118961

Simplifying
t + -3.75 = 3.913118961

Reorder the terms:
-3.75 + t = 3.913118961

Solving
-3.75 + t = 3.913118961

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 3.913118961 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 3.913118961 + 3.75
t = 3.913118961 + 3.75

Combine like terms: 3.913118961 + 3.75 = 7.663118961
t = 7.663118961

Simplifying
t = 7.663118961

Subproblem 2
t + -3.75 = -3.913118961

Simplifying
t + -3.75 = -3.913118961

Reorder the terms:
-3.75 + t = -3.913118961

Solving
-3.75 + t = -3.913118961

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -3.913118961 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -3.913118961 + 3.75
t = -3.913118961 + 3.75

Combine like terms: -3.913118961 + 3.75 = -0.163118961
t = -0.163118961

Simplifying
t = -0.163118961

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.663118961, -0.163118961}
Solution
t = {7.663118961, -0.163118961}