9x^2=30x+72

Solution for 9x^2=30x+72 equation:

Simplifying
9x2 = 30x + 72

Reorder the terms:
9x2 = 72 + 30x

Solving
9x2 = 72 + 30x

Solving for variable 'x'.

Reorder the terms:
-72 + -30x + 9x2 = 72 + 30x + -72 + -30x

Reorder the terms:
-72 + -30x + 9x2 = 72 + -72 + 30x + -30x

Combine like terms: 72 + -72 = 0
-72 + -30x + 9x2 = 0 + 30x + -30x
-72 + -30x + 9x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-72 + -30x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -10x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-24 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
-24 + -10x + 3x2 = 0

Solving
-24 + -10x + 3x2 = 0

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

Divide each side by '3'.
-8 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3.333333333x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -3.333333333x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3.333333333x + x2 = 0 + 8
-3.333333333x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3.333333333x + x2 = 8

The x term is -3.333333333x.  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.
-3.333333333x + 2.777777779 + x2 = 8 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 8 + 2.777777779

Combine like terms: 8 + 2.777777779 = 10.777777779
2.777777779 + -3.333333333x + x2 = 10.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 10.777777779

Calculate the square root of the right side: 3.282952601

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.282952601 and -3.282952601.

Subproblem 1
x + -1.666666667 = 3.282952601

Simplifying
x + -1.666666667 = 3.282952601

Reorder the terms:
-1.666666667 + x = 3.282952601

Solving
-1.666666667 + x = 3.282952601

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.282952601 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.282952601 + 1.666666667
x = 3.282952601 + 1.666666667

Combine like terms: 3.282952601 + 1.666666667 = 4.949619268
x = 4.949619268

Simplifying
x = 4.949619268

Subproblem 2
x + -1.666666667 = -3.282952601

Simplifying
x + -1.666666667 = -3.282952601

Reorder the terms:
-1.666666667 + x = -3.282952601

Solving
-1.666666667 + x = -3.282952601

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.282952601 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.282952601 + 1.666666667
x = -3.282952601 + 1.666666667

Combine like terms: -3.282952601 + 1.666666667 = -1.616285934
x = -1.616285934

Simplifying
x = -1.616285934

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.949619268, -1.616285934}
Solution
x = {4.949619268, -1.616285934}