f(f-5)=3(f-5)

Solution for f(f-5)=3(f-5) equation:

f(f-5)=3(f-5)

We move all terms to the left:

f(f-5)-(3(f-5))=0

We multiply parentheses

f^2-5f-(3(f-5))=0


We calculate terms in parentheses: -(3(f-5)), so:

3(f-5)

We multiply parentheses

3f-15

Back to the equation:

-(3f-15)


We get rid of parentheses

f^2-5f-3f+15=0

We add all the numbers together, and all the variables

f^2-8f+15=0

a = 1; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*1}=\frac{6}{2}
=3
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*1}=\frac{10}{2}
=5
$