0=(9t^2)-(12t)-4

Solution for 0=(9t^2)-(12t)-4 equation:

Simplifying
0 = (9t2) + -1(12t) + -4

Remove parenthesis around (12t)
0 = (9t2) + -1 * 12t + -4

Multiply -1 * 12
0 = (9t2) + -12t + -4

Reorder the terms:
0 = -4 + -12t + (9t2)

Solving
0 = -4 + -12t + (9t2)

Solving for variable 't'.

Combine like terms: 0 + 4 = 4
4 + 12t + (-9t2) = -4 + -12t + (9t2) + 4 + 12t + (-9t2)

Reorder the terms:
4 + 12t + (-9t2) = -4 + 4 + -12t + 12t + (9t2) + (-9t2)

Combine like terms: -4 + 4 = 0
4 + 12t + (-9t2) = 0 + -12t + 12t + (9t2) + (-9t2)
4 + 12t + (-9t2) = -12t + 12t + (9t2) + (-9t2)

Combine like terms: -12t + 12t = 0
4 + 12t + (-9t2) = 0 + (9t2) + (-9t2)
4 + 12t + (-9t2) = (9t2) + (-9t2)

Combine like terms: (9t2) + (-9t2) = 0
4 + 12t + (-9t2) = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.4444444444 + -1.333333333t + t2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -1.333333333t + 0.4444444444 + t2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -1.333333333t + t2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -1.333333333t + t2 = 0 + 0.4444444444
-1.333333333t + t2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-1.333333333t + t2 = 0.4444444444

The t term is -1.333333333t.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333t + 0.4444444442 + t2 = 0.4444444444 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333t + t2 = 0.4444444444 + 0.4444444442

Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886
0.4444444442 + -1.333333333t + t2 = 0.8888888886

Factor a perfect square on the left side:
((t) + -0.6666666665)((t) + -0.6666666665) = 0.8888888886

Calculate the square root of the right side: 0.942809041

Break this problem into two subproblems by setting 
((t) + -0.6666666665) equal to 0.942809041 and -0.942809041.

Subproblem 1
(t) + -0.6666666665 = 0.942809041

Simplifying
(t) + -0.6666666665 = 0.942809041
t + -0.6666666665 = 0.942809041

Reorder the terms:
-0.6666666665 + t = 0.942809041

Solving
-0.6666666665 + t = 0.942809041

Solving for variable 't'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + t = 0.942809041 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + t = 0.942809041 + 0.6666666665
t = 0.942809041 + 0.6666666665

Combine like terms: 0.942809041 + 0.6666666665 = 1.6094757075
t = 1.6094757075

Simplifying
t = 1.6094757075

Subproblem 2
(t) + -0.6666666665 = -0.942809041

Simplifying
(t) + -0.6666666665 = -0.942809041
t + -0.6666666665 = -0.942809041

Reorder the terms:
-0.6666666665 + t = -0.942809041

Solving
-0.6666666665 + t = -0.942809041

Solving for variable 't'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + t = -0.942809041 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + t = -0.942809041 + 0.6666666665
t = -0.942809041 + 0.6666666665

Combine like terms: -0.942809041 + 0.6666666665 = -0.2761423745
t = -0.2761423745

Simplifying
t = -0.2761423745

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.6094757075, -0.2761423745}