5=9f+2f^2

Solution for 5=9f+2f^2 equation:

Simplifying
5 = 9f + 2f2

Solving
5 = 9f + 2f2

Solving for variable 'f'.

Reorder the terms:
5 + -9f + -2f2 = 9f + -9f + 2f2 + -2f2

Combine like terms: 9f + -9f = 0
5 + -9f + -2f2 = 0 + 2f2 + -2f2
5 + -9f + -2f2 = 2f2 + -2f2

Combine like terms: 2f2 + -2f2 = 0
5 + -9f + -2f2 = 0

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

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

Simplifying
1 + -2f = 0

Solving
1 + -2f = 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 + -2f = 0 + -1

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

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

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

Simplifying
f = 0.5
Subproblem 2
Set the factor '(5 + f)' equal to zero and attempt to solve:

Simplifying
5 + f = 0

Solving
5 + f = 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 + f = 0 + -5

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

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

Simplifying
f = -5
Solution
f = {0.5, -5}