9t^2-20t-12=0

Solution for 9t^2-20t-12=0 equation:

Simplifying
9t2 + -20t + -12 = 0

Reorder the terms:
-12 + -20t + 9t2 = 0

Solving
-12 + -20t + 9t2 = 0

Solving for variable 't'.

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

Divide each side by '9'.
-1.333333333 + -2.222222222t + t2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2.222222222t + 1.333333333 + t2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2.222222222t + t2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2.222222222t + t2 = 0 + 1.333333333
-2.222222222t + t2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2.222222222t + t2 = 1.333333333

The t term is -2.222222222t.  Take half its coefficient (-1.111111111).
Square it (1.234567901) and add it to both sides.

Add '1.234567901' to each side of the equation.
-2.222222222t + 1.234567901 + t2 = 1.333333333 + 1.234567901

Reorder the terms:
1.234567901 + -2.222222222t + t2 = 1.333333333 + 1.234567901

Combine like terms: 1.333333333 + 1.234567901 = 2.567901234
1.234567901 + -2.222222222t + t2 = 2.567901234

Factor a perfect square on the left side:
(t + -1.111111111)(t + -1.111111111) = 2.567901234

Calculate the square root of the right side: 1.602467233

Break this problem into two subproblems by setting 
(t + -1.111111111) equal to 1.602467233 and -1.602467233.

Subproblem 1
t + -1.111111111 = 1.602467233

Simplifying
t + -1.111111111 = 1.602467233

Reorder the terms:
-1.111111111 + t = 1.602467233

Solving
-1.111111111 + t = 1.602467233

Solving for variable 't'.

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

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.111111111 + t = 1.602467233 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + t = 1.602467233 + 1.111111111
t = 1.602467233 + 1.111111111

Combine like terms: 1.602467233 + 1.111111111 = 2.713578344
t = 2.713578344

Simplifying
t = 2.713578344

Subproblem 2
t + -1.111111111 = -1.602467233

Simplifying
t + -1.111111111 = -1.602467233

Reorder the terms:
-1.111111111 + t = -1.602467233

Solving
-1.111111111 + t = -1.602467233

Solving for variable 't'.

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

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.111111111 + t = -1.602467233 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + t = -1.602467233 + 1.111111111
t = -1.602467233 + 1.111111111

Combine like terms: -1.602467233 + 1.111111111 = -0.491356122
t = -0.491356122

Simplifying
t = -0.491356122

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.713578344, -0.491356122}