4f^2-f-5=0

Solution for 4f^2-f-5=0 equation:

Simplifying
4f2 + -1f + -5 = 0

Reorder the terms:
-5 + -1f + 4f2 = 0

Solving
-5 + -1f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -1f)(5 + -4f) = 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 + -4f)' equal to zero and attempt to solve:

Simplifying
5 + -4f = 0

Solving
5 + -4f = 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 + -4f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4f = 0 + -5
-4f = 0 + -5

Combine like terms: 0 + -5 = -5
-4f = -5

Divide each side by '-4'.
f = 1.25

Simplifying
f = 1.25
Solution
f = {-1, 1.25}