4f^2-9f+2=0

Solution for 4f^2-9f+2=0 equation:

Simplifying
4f2 + -9f + 2 = 0

Reorder the terms:
2 + -9f + 4f2 = 0

Solving
2 + -9f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(1 + -4f)(2 + -1f) = 0

Subproblem 1
Set the factor '(1 + -4f)' equal to zero and attempt to solve:

Simplifying
1 + -4f = 0

Solving
1 + -4f = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4f = 0 + -1
-4f = 0 + -1

Combine like terms: 0 + -1 = -1
-4f = -1

Divide each side by '-4'.
f = 0.25

Simplifying
f = 0.25
Subproblem 2
Set the factor '(2 + -1f)' equal to zero and attempt to solve:

Simplifying
2 + -1f = 0

Solving
2 + -1f = 0

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

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

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

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

Divide each side by '-1'.
f = 2

Simplifying
f = 2
Solution
f = {0.25, 2}