9x^2-53x+78=0

Solution for 9x^2-53x+78=0 equation:

Simplifying
9x2 + -53x + 78 = 0

Reorder the terms:
78 + -53x + 9x2 = 0

Solving
78 + -53x + 9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(26 + -9x)(3 + -1x) = 0

Subproblem 1
Set the factor '(26 + -9x)' equal to zero and attempt to solve:

Simplifying
26 + -9x = 0

Solving
26 + -9x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -9x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -9x = 0 + -26
-9x = 0 + -26

Combine like terms: 0 + -26 = -26
-9x = -26

Divide each side by '-9'.
x = 2.888888889

Simplifying
x = 2.888888889
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2.888888889, 3}