1.5=-16t^2+48t

Solution for 1.5=-16t^2+48t equation:

Simplifying
1.5 = -16t2 + 48t

Reorder the terms:
1.5 = 48t + -16t2

Solving
1.5 = 48t + -16t2

Solving for variable 't'.

Reorder the terms:
1.5 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
1.5 + -48t + 16t2 = 0 + -16t2 + 16t2
1.5 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
1.5 + -48t + 16t2 = 0

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

Divide each side by '16'.
0.09375 + -3t + t2 = 0

Move the constant term to the right:

Add '-0.09375' to each side of the equation.
0.09375 + -3t + -0.09375 + t2 = 0 + -0.09375

Reorder the terms:
0.09375 + -0.09375 + -3t + t2 = 0 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + -3t + t2 = 0 + -0.09375
-3t + t2 = 0 + -0.09375

Combine like terms: 0 + -0.09375 = -0.09375
-3t + t2 = -0.09375

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -0.09375 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -0.09375 + 2.25

Combine like terms: -0.09375 + 2.25 = 2.15625
2.25 + -3t + t2 = 2.15625

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 2.15625

Calculate the square root of the right side: 1.468417516

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.468417516 and -1.468417516.

Subproblem 1
t + -1.5 = 1.468417516

Simplifying
t + -1.5 = 1.468417516

Reorder the terms:
-1.5 + t = 1.468417516

Solving
-1.5 + t = 1.468417516

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.468417516 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.468417516 + 1.5
t = 1.468417516 + 1.5

Combine like terms: 1.468417516 + 1.5 = 2.968417516
t = 2.968417516

Simplifying
t = 2.968417516

Subproblem 2
t + -1.5 = -1.468417516

Simplifying
t + -1.5 = -1.468417516

Reorder the terms:
-1.5 + t = -1.468417516

Solving
-1.5 + t = -1.468417516

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.468417516 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.468417516 + 1.5
t = -1.468417516 + 1.5

Combine like terms: -1.468417516 + 1.5 = 0.031582484
t = 0.031582484

Simplifying
t = 0.031582484

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.968417516, 0.031582484}