9t^2-3=11t

Solution for 9t^2-3=11t equation:

Simplifying
9t2 + -3 = 11t

Reorder the terms:
-3 + 9t2 = 11t

Solving
-3 + 9t2 = 11t

Solving for variable 't'.

Reorder the terms:
-3 + -11t + 9t2 = 11t + -11t

Combine like terms: 11t + -11t = 0
-3 + -11t + 9t2 = 0

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

Divide each side by '9'.
-0.3333333333 + -1.222222222t + t2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -1.222222222t + 0.3333333333 + t2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -1.222222222t + t2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -1.222222222t + t2 = 0 + 0.3333333333
-1.222222222t + t2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-1.222222222t + t2 = 0.3333333333

The t term is -1.222222222t.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222t + 0.3734567900 + t2 = 0.3333333333 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222t + t2 = 0.3333333333 + 0.3734567900

Combine like terms: 0.3333333333 + 0.3734567900 = 0.7067901233
0.3734567900 + -1.222222222t + t2 = 0.7067901233

Factor a perfect square on the left side:
(t + -0.611111111)(t + -0.611111111) = 0.7067901233

Calculate the square root of the right side: 0.840708108

Break this problem into two subproblems by setting 
(t + -0.611111111) equal to 0.840708108 and -0.840708108.

Subproblem 1
t + -0.611111111 = 0.840708108

Simplifying
t + -0.611111111 = 0.840708108

Reorder the terms:
-0.611111111 + t = 0.840708108

Solving
-0.611111111 + t = 0.840708108

Solving for variable 't'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + t = 0.840708108 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + t = 0.840708108 + 0.611111111
t = 0.840708108 + 0.611111111

Combine like terms: 0.840708108 + 0.611111111 = 1.451819219
t = 1.451819219

Simplifying
t = 1.451819219

Subproblem 2
t + -0.611111111 = -0.840708108

Simplifying
t + -0.611111111 = -0.840708108

Reorder the terms:
-0.611111111 + t = -0.840708108

Solving
-0.611111111 + t = -0.840708108

Solving for variable 't'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + t = -0.840708108 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + t = -0.840708108 + 0.611111111
t = -0.840708108 + 0.611111111

Combine like terms: -0.840708108 + 0.611111111 = -0.229596997
t = -0.229596997

Simplifying
t = -0.229596997

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.451819219, -0.229596997}