9t^2+15t-136=0

Solution for 9t^2+15t-136=0 equation:

Simplifying
9t2 + 15t + -136 = 0

Reorder the terms:
-136 + 15t + 9t2 = 0

Solving
-136 + 15t + 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'.
-15.11111111 + 1.666666667t + t2 = 0

Move the constant term to the right:

Add '15.11111111' to each side of the equation.
-15.11111111 + 1.666666667t + 15.11111111 + t2 = 0 + 15.11111111

Reorder the terms:
-15.11111111 + 15.11111111 + 1.666666667t + t2 = 0 + 15.11111111

Combine like terms: -15.11111111 + 15.11111111 = 0.00000000
0.00000000 + 1.666666667t + t2 = 0 + 15.11111111
1.666666667t + t2 = 0 + 15.11111111

Combine like terms: 0 + 15.11111111 = 15.11111111
1.666666667t + t2 = 15.11111111

The t term is 1.666666667t.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667t + 0.6944444447 + t2 = 15.11111111 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667t + t2 = 15.11111111 + 0.6944444447

Combine like terms: 15.11111111 + 0.6944444447 = 15.8055555547
0.6944444447 + 1.666666667t + t2 = 15.8055555547

Factor a perfect square on the left side:
(t + 0.8333333335)(t + 0.8333333335) = 15.8055555547

Calculate the square root of the right side: 3.975620147

Break this problem into two subproblems by setting 
(t + 0.8333333335) equal to 3.975620147 and -3.975620147.

Subproblem 1
t + 0.8333333335 = 3.975620147

Simplifying
t + 0.8333333335 = 3.975620147

Reorder the terms:
0.8333333335 + t = 3.975620147

Solving
0.8333333335 + t = 3.975620147

Solving for variable 't'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + t = 3.975620147 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + t = 3.975620147 + -0.8333333335
t = 3.975620147 + -0.8333333335

Combine like terms: 3.975620147 + -0.8333333335 = 3.1422868135
t = 3.1422868135

Simplifying
t = 3.1422868135

Subproblem 2
t + 0.8333333335 = -3.975620147

Simplifying
t + 0.8333333335 = -3.975620147

Reorder the terms:
0.8333333335 + t = -3.975620147

Solving
0.8333333335 + t = -3.975620147

Solving for variable 't'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + t = -3.975620147 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + t = -3.975620147 + -0.8333333335
t = -3.975620147 + -0.8333333335

Combine like terms: -3.975620147 + -0.8333333335 = -4.8089534805
t = -4.8089534805

Simplifying
t = -4.8089534805

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.1422868135, -4.8089534805}