F(x)=6x(x-9)

Solution for F(x)=6x(x-9) equation:

(F)=6F(F-9)

We move all terms to the left:

(F)-(6F(F-9))=0


We calculate terms in parentheses: -(6F(F-9)), so:

6F(F-9)

We multiply parentheses

6F^2-54F

Back to the equation:

-(6F^2-54F)


We get rid of parentheses

-6F^2+F+54F=0

We add all the numbers together, and all the variables

-6F^2+55F=0

a = -6; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-6)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*-6}=\frac{-110}{-12}
=9+1/6
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-6}=\frac{0}{-12}
=0
$