f(f-2)=4f

Solution for f(f-2)=4f equation:

f(f-2)=4f

We move all terms to the left:

f(f-2)-(4f)=0

We add all the numbers together, and all the variables

-4f+f(f-2)=0

We multiply parentheses

f^2-4f-2f=0

We add all the numbers together, and all the variables

f^2-6f=0

a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2}
=6
$