4x^2-114x+470=0

Solution for 4x^2-114x+470=0 equation:

Simplifying
4x2 + -114x + 470 = 0

Reorder the terms:
470 + -114x + 4x2 = 0

Solving
470 + -114x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(235 + -57x + 2x2) = 0

Factor a trinomial.
2((5 + -1x)(47 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(47 + -2x)' equal to zero and attempt to solve:

Simplifying
47 + -2x = 0

Solving
47 + -2x = 0

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

Add '-47' to each side of the equation.
47 + -47 + -2x = 0 + -47

Combine like terms: 47 + -47 = 0
0 + -2x = 0 + -47
-2x = 0 + -47

Combine like terms: 0 + -47 = -47
-2x = -47

Divide each side by '-2'.
x = 23.5

Simplifying
x = 23.5
Solution
x = {5, 23.5}