20=16t^2+30t+4.5

Solution for 20=16t^2+30t+4.5 equation:

Simplifying
20 = 16t2 + 30t + 4.5

Reorder the terms:
20 = 4.5 + 30t + 16t2

Solving
20 = 4.5 + 30t + 16t2

Solving for variable 't'.

Combine like terms: 20 + -4.5 = 15.5
15.5 + -30t + -16t2 = 4.5 + 30t + 16t2 + -4.5 + -30t + -16t2

Reorder the terms:
15.5 + -30t + -16t2 = 4.5 + -4.5 + 30t + -30t + 16t2 + -16t2

Combine like terms: 4.5 + -4.5 = 0.0
15.5 + -30t + -16t2 = 0.0 + 30t + -30t + 16t2 + -16t2
15.5 + -30t + -16t2 = 30t + -30t + 16t2 + -16t2

Combine like terms: 30t + -30t = 0
15.5 + -30t + -16t2 = 0 + 16t2 + -16t2
15.5 + -30t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
15.5 + -30t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.96875 + 1.875t + t2 = 0

Move the constant term to the right:

Add '0.96875' to each side of the equation.
-0.96875 + 1.875t + 0.96875 + t2 = 0 + 0.96875

Reorder the terms:
-0.96875 + 0.96875 + 1.875t + t2 = 0 + 0.96875

Combine like terms: -0.96875 + 0.96875 = 0.00000
0.00000 + 1.875t + t2 = 0 + 0.96875
1.875t + t2 = 0 + 0.96875

Combine like terms: 0 + 0.96875 = 0.96875
1.875t + t2 = 0.96875

The t term is 1.875t.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875t + 0.87890625 + t2 = 0.96875 + 0.87890625

Reorder the terms:
0.87890625 + 1.875t + t2 = 0.96875 + 0.87890625

Combine like terms: 0.96875 + 0.87890625 = 1.84765625
0.87890625 + 1.875t + t2 = 1.84765625

Factor a perfect square on the left side:
(t + 0.9375)(t + 0.9375) = 1.84765625

Calculate the square root of the right side: 1.359285198

Break this problem into two subproblems by setting 
(t + 0.9375) equal to 1.359285198 and -1.359285198.

Subproblem 1
t + 0.9375 = 1.359285198

Simplifying
t + 0.9375 = 1.359285198

Reorder the terms:
0.9375 + t = 1.359285198

Solving
0.9375 + t = 1.359285198

Solving for variable 't'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + t = 1.359285198 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = 1.359285198 + -0.9375
t = 1.359285198 + -0.9375

Combine like terms: 1.359285198 + -0.9375 = 0.421785198
t = 0.421785198

Simplifying
t = 0.421785198

Subproblem 2
t + 0.9375 = -1.359285198

Simplifying
t + 0.9375 = -1.359285198

Reorder the terms:
0.9375 + t = -1.359285198

Solving
0.9375 + t = -1.359285198

Solving for variable 't'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + t = -1.359285198 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + t = -1.359285198 + -0.9375
t = -1.359285198 + -0.9375

Combine like terms: -1.359285198 + -0.9375 = -2.296785198
t = -2.296785198

Simplifying
t = -2.296785198

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.421785198, -2.296785198}