72w^2-17w+1=0

Solution for 72w^2-17w+1=0 equation:

Simplifying
72w2 + -17w + 1 = 0

Reorder the terms:
1 + -17w + 72w2 = 0

Solving
1 + -17w + 72w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -9w)(1 + -8w) = 0

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

Simplifying
1 + -9w = 0

Solving
1 + -9w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -9w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9w = 0 + -1
-9w = 0 + -1

Combine like terms: 0 + -1 = -1
-9w = -1

Divide each side by '-9'.
w = 0.1111111111

Simplifying
w = 0.1111111111
Subproblem 2
Set the factor '(1 + -8w)' equal to zero and attempt to solve:

Simplifying
1 + -8w = 0

Solving
1 + -8w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8w = 0 + -1
-8w = 0 + -1

Combine like terms: 0 + -1 = -1
-8w = -1

Divide each side by '-8'.
w = 0.125

Simplifying
w = 0.125
Solution
w = {0.1111111111, 0.125}