7t^2-6t-9=0

Solution for 7t^2-6t-9=0 equation:

Simplifying
7t2 + -6t + -9 = 0

Reorder the terms:
-9 + -6t + 7t2 = 0

Solving
-9 + -6t + 7t2 = 0

Solving for variable 't'.

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

Divide each side by '7'.
-1.285714286 + -0.8571428571t + t2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -0.8571428571t + 1.285714286 + t2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -0.8571428571t + t2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -0.8571428571t + t2 = 0 + 1.285714286
-0.8571428571t + t2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-0.8571428571t + t2 = 1.285714286

The t term is -0.8571428571t.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571t + 0.1836734694 + t2 = 1.285714286 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571t + t2 = 1.285714286 + 0.1836734694

Combine like terms: 1.285714286 + 0.1836734694 = 1.4693877554
0.1836734694 + -0.8571428571t + t2 = 1.4693877554

Factor a perfect square on the left side:
(t + -0.4285714286)(t + -0.4285714286) = 1.4693877554

Calculate the square root of the right side: 1.212183054

Break this problem into two subproblems by setting 
(t + -0.4285714286) equal to 1.212183054 and -1.212183054.

Subproblem 1
t + -0.4285714286 = 1.212183054

Simplifying
t + -0.4285714286 = 1.212183054

Reorder the terms:
-0.4285714286 + t = 1.212183054

Solving
-0.4285714286 + t = 1.212183054

Solving for variable 't'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + t = 1.212183054 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + t = 1.212183054 + 0.4285714286
t = 1.212183054 + 0.4285714286

Combine like terms: 1.212183054 + 0.4285714286 = 1.6407544826
t = 1.6407544826

Simplifying
t = 1.6407544826

Subproblem 2
t + -0.4285714286 = -1.212183054

Simplifying
t + -0.4285714286 = -1.212183054

Reorder the terms:
-0.4285714286 + t = -1.212183054

Solving
-0.4285714286 + t = -1.212183054

Solving for variable 't'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + t = -1.212183054 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + t = -1.212183054 + 0.4285714286
t = -1.212183054 + 0.4285714286

Combine like terms: -1.212183054 + 0.4285714286 = -0.7836116254
t = -0.7836116254

Simplifying
t = -0.7836116254

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.6407544826, -0.7836116254}