(-18x^2)+43x-17=0

Solution for (-18x^2)+43x-17=0 equation:

Simplifying
(-18x2) + 43x + -17 = 0

Reorder the terms:
-17 + 43x + (-18x2) = 0

Solving
-17 + 43x + (-18x2) = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + 9x)(1 + -2x) = 0

Subproblem 1
Set the factor '(-17 + 9x)' equal to zero and attempt to solve:

Simplifying
-17 + 9x = 0

Solving
-17 + 9x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 9x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 9x = 0 + 17
9x = 0 + 17

Combine like terms: 0 + 17 = 17
9x = 17

Divide each side by '9'.
x = 1.888888889

Simplifying
x = 1.888888889
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {1.888888889, 0.5}