F(x)=(2x-4)(x-6)

Solution for F(x)=(2x-4)(x-6) equation:

(F)=(2F-4)(F-6)

We move all terms to the left:

(F)-((2F-4)(F-6))=0

We multiply parentheses ..

-((+2F^2-12F-4F+24))+F=0


We calculate terms in parentheses: -((+2F^2-12F-4F+24)), so:

(+2F^2-12F-4F+24)

We get rid of parentheses

2F^2-12F-4F+24

We add all the numbers together, and all the variables

2F^2-16F+24

Back to the equation:

-(2F^2-16F+24)


We add all the numbers together, and all the variables

F-(2F^2-16F+24)=0

We get rid of parentheses

-2F^2+F+16F-24=0

We add all the numbers together, and all the variables

-2F^2+17F-24=0

a = -2; b = 17; c = -24;
Δ = b2-4ac
Δ = 172-4·(-2)·(-24)
Δ = 97
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{-(17)-\sqrt{97}}{2*-2}=\frac{-17-\sqrt{97}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{97}}{2*-2}=\frac{-17+\sqrt{97}}{-4}
$