21-9f=20f(f-6)

Solution for 21-9f=20f(f-6) equation:

21-9f=20f(f-6)

We move all terms to the left:

21-9f-(20f(f-6))=0


We calculate terms in parentheses: -(20f(f-6)), so:

20f(f-6)

We multiply parentheses

20f^2-120f

Back to the equation:

-(20f^2-120f)


We get rid of parentheses

-20f^2-9f+120f+21=0

We add all the numbers together, and all the variables

-20f^2+111f+21=0

a = -20; b = 111; c = +21;
Δ = b2-4ac
Δ = 1112-4·(-20)·21
Δ = 14001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-\sqrt{14001}}{2*-20}=\frac{-111-\sqrt{14001}}{-40}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+\sqrt{14001}}{2*-20}=\frac{-111+\sqrt{14001}}{-40}
$