f-6=-2f+3f(f-2)

Solution for f-6=-2f+3f(f-2) equation:

f-6=-2f+3f(f-2)

We move all terms to the left:

f-6-(-2f+3f(f-2))=0


We calculate terms in parentheses: -(-2f+3f(f-2)), so:

-2f+3f(f-2)

We multiply parentheses

3f^2-2f-6f

We add all the numbers together, and all the variables

3f^2-8f

Back to the equation:

-(3f^2-8f)


We get rid of parentheses

-3f^2+f+8f-6=0

We add all the numbers together, and all the variables

-3f^2+9f-6=0

a = -3; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-3)·(-6)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-3}=\frac{-12}{-6}
=+2
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-3}=\frac{-6}{-6}
=1
$