9t^2+30t-7=0

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Solution for 9t^2+30t-7=0 equation: 


Simplifying
9t2 + 30t + -7 = 0

Reorder the terms:
-7 + 30t + 9t2 = 0

Solving
-7 + 30t + 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'.
-0.7777777778 + 3.333333333t + t2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + 3.333333333t + 0.7777777778 + t2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + 3.333333333t + t2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + 3.333333333t + t2 = 0 + 0.7777777778
3.333333333t + t2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
3.333333333t + t2 = 0.7777777778

The t term is 3.333333333t.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333t + 2.777777779 + t2 = 0.7777777778 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333t + t2 = 0.7777777778 + 2.777777779

Combine like terms: 0.7777777778 + 2.777777779 = 3.5555555568
2.777777779 + 3.333333333t + t2 = 3.5555555568

Factor a perfect square on the left side:
(t + 1.666666667)(t + 1.666666667) = 3.5555555568

Calculate the square root of the right side: 1.885618083

Break this problem into two subproblems by setting 
(t + 1.666666667) equal to 1.885618083 and -1.885618083.


Subproblem 1
t + 1.666666667 = 1.885618083

Simplifying
t + 1.666666667 = 1.885618083

Reorder the terms:
1.666666667 + t = 1.885618083

Solving
1.666666667 + t = 1.885618083

Solving for variable 't'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + t = 1.885618083 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + t = 1.885618083 + -1.666666667
t = 1.885618083 + -1.666666667

Combine like terms: 1.885618083 + -1.666666667 = 0.218951416
t = 0.218951416

Simplifying
t = 0.218951416


Subproblem 2
t + 1.666666667 = -1.885618083

Simplifying
t + 1.666666667 = -1.885618083

Reorder the terms:
1.666666667 + t = -1.885618083

Solving
1.666666667 + t = -1.885618083

Solving for variable 't'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + t = -1.885618083 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + t = -1.885618083 + -1.666666667
t = -1.885618083 + -1.666666667

Combine like terms: -1.885618083 + -1.666666667 = -3.55228475
t = -3.55228475

Simplifying
t = -3.55228475


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.218951416, -3.55228475}

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