3f^2-8f+5=0

Solution for 3f^2-8f+5=0 equation:

Simplifying
3f2 + -8f + 5 = 0

Reorder the terms:
5 + -8f + 3f2 = 0

Solving
5 + -8f + 3f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(1 + -1f)(5 + -3f) = 0

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

Simplifying
1 + -1f = 0

Solving
1 + -1f = 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 + -1f = 0 + -1

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

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

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

Simplifying
f = 1
Subproblem 2
Set the factor '(5 + -3f)' equal to zero and attempt to solve:

Simplifying
5 + -3f = 0

Solving
5 + -3f = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3f = 0 + -5
-3f = 0 + -5

Combine like terms: 0 + -5 = -5
-3f = -5

Divide each side by '-3'.
f = 1.666666667

Simplifying
f = 1.666666667
Solution
f = {1, 1.666666667}