5f^2+4=f+6

Solution for 5f^2+4=f+6 equation:

Simplifying
5f2 + 4 = f + 6

Reorder the terms:
4 + 5f2 = f + 6

Reorder the terms:
4 + 5f2 = 6 + f

Solving
4 + 5f2 = 6 + f

Solving for variable 'f'.

Reorder the terms:
4 + -6 + -1f + 5f2 = 6 + f + -6 + -1f

Combine like terms: 4 + -6 = -2
-2 + -1f + 5f2 = 6 + f + -6 + -1f

Reorder the terms:
-2 + -1f + 5f2 = 6 + -6 + f + -1f

Combine like terms: 6 + -6 = 0
-2 + -1f + 5f2 = 0 + f + -1f
-2 + -1f + 5f2 = f + -1f

Combine like terms: f + -1f = 0
-2 + -1f + 5f2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.4 + -0.2f + f2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.2f + 0.4 + f2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.2f + f2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.2f + f2 = 0 + 0.4
-0.2f + f2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.2f + f2 = 0.4

The f term is -0.2f.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2f + 0.01 + f2 = 0.4 + 0.01

Reorder the terms:
0.01 + -0.2f + f2 = 0.4 + 0.01

Combine like terms: 0.4 + 0.01 = 0.41
0.01 + -0.2f + f2 = 0.41

Factor a perfect square on the left side:
(f + -0.1)(f + -0.1) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(f + -0.1) equal to 0.640312424 and -0.640312424.

Subproblem 1
f + -0.1 = 0.640312424

Simplifying
f + -0.1 = 0.640312424

Reorder the terms:
-0.1 + f = 0.640312424

Solving
-0.1 + f = 0.640312424

Solving for variable 'f'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + f = 0.640312424 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + f = 0.640312424 + 0.1
f = 0.640312424 + 0.1

Combine like terms: 0.640312424 + 0.1 = 0.740312424
f = 0.740312424

Simplifying
f = 0.740312424

Subproblem 2
f + -0.1 = -0.640312424

Simplifying
f + -0.1 = -0.640312424

Reorder the terms:
-0.1 + f = -0.640312424

Solving
-0.1 + f = -0.640312424

Solving for variable 'f'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + f = -0.640312424 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + f = -0.640312424 + 0.1
f = -0.640312424 + 0.1

Combine like terms: -0.640312424 + 0.1 = -0.540312424
f = -0.540312424

Simplifying
f = -0.540312424

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.740312424, -0.540312424}