48=-4t^2+48t+3

Solution for 48=-4t^2+48t+3 equation:

Simplifying
48 = -4t2 + 48t + 3

Reorder the terms:
48 = 3 + 48t + -4t2

Solving
48 = 3 + 48t + -4t2

Solving for variable 't'.

Combine like terms: 48 + -3 = 45
45 + -48t + 4t2 = 3 + 48t + -4t2 + -3 + -48t + 4t2

Reorder the terms:
45 + -48t + 4t2 = 3 + -3 + 48t + -48t + -4t2 + 4t2

Combine like terms: 3 + -3 = 0
45 + -48t + 4t2 = 0 + 48t + -48t + -4t2 + 4t2
45 + -48t + 4t2 = 48t + -48t + -4t2 + 4t2

Combine like terms: 48t + -48t = 0
45 + -48t + 4t2 = 0 + -4t2 + 4t2
45 + -48t + 4t2 = -4t2 + 4t2

Combine like terms: -4t2 + 4t2 = 0
45 + -48t + 4t2 = 0

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

Divide each side by '4'.
11.25 + -12t + t2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + -12t + -11.25 + t2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + -12t + t2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + -12t + t2 = 0 + -11.25
-12t + t2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
-12t + t2 = -11.25

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -11.25 + 36

Reorder the terms:
36 + -12t + t2 = -11.25 + 36

Combine like terms: -11.25 + 36 = 24.75
36 + -12t + t2 = 24.75

Factor a perfect square on the left side:
(t + -6)(t + -6) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(t + -6) equal to 4.974937186 and -4.974937186.

Subproblem 1
t + -6 = 4.974937186

Simplifying
t + -6 = 4.974937186

Reorder the terms:
-6 + t = 4.974937186

Solving
-6 + t = 4.974937186

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = 4.974937186 + 6

Combine like terms: -6 + 6 = 0
0 + t = 4.974937186 + 6
t = 4.974937186 + 6

Combine like terms: 4.974937186 + 6 = 10.974937186
t = 10.974937186

Simplifying
t = 10.974937186

Subproblem 2
t + -6 = -4.974937186

Simplifying
t + -6 = -4.974937186

Reorder the terms:
-6 + t = -4.974937186

Solving
-6 + t = -4.974937186

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = -4.974937186 + 6

Combine like terms: -6 + 6 = 0
0 + t = -4.974937186 + 6
t = -4.974937186 + 6

Combine like terms: -4.974937186 + 6 = 1.025062814
t = 1.025062814

Simplifying
t = 1.025062814

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.974937186, 1.025062814}