9x^2-97x+234=0

Solution for 9x^2-97x+234=0 equation:

Simplifying
9x2 + -97x + 234 = 0

Reorder the terms:
234 + -97x + 9x2 = 0

Solving
234 + -97x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
26 + -10.77777778x + x2 = 0

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -10.77777778x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + -10.77777778x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -10.77777778x + x2 = 0 + -26
-10.77777778x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
-10.77777778x + x2 = -26

The x term is -10.77777778x.  Take half its coefficient (-5.38888889).
Square it (29.04012347) and add it to both sides.

Add '29.04012347' to each side of the equation.
-10.77777778x + 29.04012347 + x2 = -26 + 29.04012347

Reorder the terms:
29.04012347 + -10.77777778x + x2 = -26 + 29.04012347

Combine like terms: -26 + 29.04012347 = 3.04012347
29.04012347 + -10.77777778x + x2 = 3.04012347

Factor a perfect square on the left side:
(x + -5.38888889)(x + -5.38888889) = 3.04012347

Calculate the square root of the right side: 1.743594985

Break this problem into two subproblems by setting 
(x + -5.38888889) equal to 1.743594985 and -1.743594985.

Subproblem 1
x + -5.38888889 = 1.743594985

Simplifying
x + -5.38888889 = 1.743594985

Reorder the terms:
-5.38888889 + x = 1.743594985

Solving
-5.38888889 + x = 1.743594985

Solving for variable 'x'.

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

Add '5.38888889' to each side of the equation.
-5.38888889 + 5.38888889 + x = 1.743594985 + 5.38888889

Combine like terms: -5.38888889 + 5.38888889 = 0.00000000
0.00000000 + x = 1.743594985 + 5.38888889
x = 1.743594985 + 5.38888889

Combine like terms: 1.743594985 + 5.38888889 = 7.132483875
x = 7.132483875

Simplifying
x = 7.132483875

Subproblem 2
x + -5.38888889 = -1.743594985

Simplifying
x + -5.38888889 = -1.743594985

Reorder the terms:
-5.38888889 + x = -1.743594985

Solving
-5.38888889 + x = -1.743594985

Solving for variable 'x'.

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

Add '5.38888889' to each side of the equation.
-5.38888889 + 5.38888889 + x = -1.743594985 + 5.38888889

Combine like terms: -5.38888889 + 5.38888889 = 0.00000000
0.00000000 + x = -1.743594985 + 5.38888889
x = -1.743594985 + 5.38888889

Combine like terms: -1.743594985 + 5.38888889 = 3.645293905
x = 3.645293905

Simplifying
x = 3.645293905

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.132483875, 3.645293905}