9t^2+2t-8=0

Solution for 9t^2+2t-8=0 equation:

Simplifying
9t2 + 2t + -8 = 0

Reorder the terms:
-8 + 2t + 9t2 = 0

Solving
-8 + 2t + 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'.
-0.8888888889 + 0.2222222222t + t2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 0.2222222222t + 0.8888888889 + t2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 0.2222222222t + t2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 0.2222222222t + t2 = 0 + 0.8888888889
0.2222222222t + t2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
0.2222222222t + t2 = 0.8888888889

The t term is 0.2222222222t.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222t + 0.01234567901 + t2 = 0.8888888889 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222t + t2 = 0.8888888889 + 0.01234567901

Combine like terms: 0.8888888889 + 0.01234567901 = 0.90123456791
0.01234567901 + 0.2222222222t + t2 = 0.90123456791

Factor a perfect square on the left side:
(t + 0.1111111111)(t + 0.1111111111) = 0.90123456791

Calculate the square root of the right side: 0.949333749

Break this problem into two subproblems by setting 
(t + 0.1111111111) equal to 0.949333749 and -0.949333749.

Subproblem 1
t + 0.1111111111 = 0.949333749

Simplifying
t + 0.1111111111 = 0.949333749

Reorder the terms:
0.1111111111 + t = 0.949333749

Solving
0.1111111111 + t = 0.949333749

Solving for variable 't'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + t = 0.949333749 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + t = 0.949333749 + -0.1111111111
t = 0.949333749 + -0.1111111111

Combine like terms: 0.949333749 + -0.1111111111 = 0.8382226379
t = 0.8382226379

Simplifying
t = 0.8382226379

Subproblem 2
t + 0.1111111111 = -0.949333749

Simplifying
t + 0.1111111111 = -0.949333749

Reorder the terms:
0.1111111111 + t = -0.949333749

Solving
0.1111111111 + t = -0.949333749

Solving for variable 't'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + t = -0.949333749 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + t = -0.949333749 + -0.1111111111
t = -0.949333749 + -0.1111111111

Combine like terms: -0.949333749 + -0.1111111111 = -1.0604448601
t = -1.0604448601

Simplifying
t = -1.0604448601

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.8382226379, -1.0604448601}