9x^2-67x+78=0

Solution for 9x^2-67x+78=0 equation:

Simplifying
9x2 + -67x + 78 = 0

Reorder the terms:
78 + -67x + 9x2 = 0

Solving
78 + -67x + 9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -9x)(6 + -1x) = 0

Subproblem 1
Set the factor '(13 + -9x)' equal to zero and attempt to solve:

Simplifying
13 + -9x = 0

Solving
13 + -9x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -9x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -9x = 0 + -13
-9x = 0 + -13

Combine like terms: 0 + -13 = -13
-9x = -13

Divide each side by '-9'.
x = 1.444444444

Simplifying
x = 1.444444444
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1.444444444, 6}