4x^2-90x+234=0

Solution for 4x^2-90x+234=0 equation:

Simplifying
4x2 + -90x + 234 = 0

Reorder the terms:
234 + -90x + 4x2 = 0

Solving
234 + -90x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(117 + -45x + 2x2) = 0

Factor a trinomial.
2((3 + -1x)(39 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(39 + -2x)' equal to zero and attempt to solve:

Simplifying
39 + -2x = 0

Solving
39 + -2x = 0

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

Add '-39' to each side of the equation.
39 + -39 + -2x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -2x = 0 + -39
-2x = 0 + -39

Combine like terms: 0 + -39 = -39
-2x = -39

Divide each side by '-2'.
x = 19.5

Simplifying
x = 19.5
Solution
x = {3, 19.5}