-5f=-3f(8-f)

Solution for -5f=-3f(8-f) equation:

-5f=-3f(8-f)

We move all terms to the left:

-5f-(-3f(8-f))=0

We add all the numbers together, and all the variables

-5f-(-3f(-1f+8))=0


We calculate terms in parentheses: -(-3f(-1f+8)), so:

-3f(-1f+8)

We multiply parentheses

3f^2-24f

Back to the equation:

-(3f^2-24f)


We get rid of parentheses

-3f^2-5f+24f=0

We add all the numbers together, and all the variables

-3f^2+19f=0

a = -3; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-3)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-3}=\frac{-38}{-6}
=6+1/3
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-3}=\frac{0}{-6}
=0
$