F=(x-1)(x-9)

Solution for F=(x-1)(x-9) equation:

=(F-1)(F-9)

We move all terms to the left:

-((F-1)(F-9))=0

We multiply parentheses ..

-((+F^2-9F-1F+9))=0


We calculate terms in parentheses: -((+F^2-9F-1F+9)), so:

(+F^2-9F-1F+9)

We get rid of parentheses

F^2-9F-1F+9

We add all the numbers together, and all the variables

F^2-10F+9

Back to the equation:

-(F^2-10F+9)


We get rid of parentheses

-F^2+10F-9=0

We add all the numbers together, and all the variables

-1F^2+10F-9=0

a = -1; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·(-1)·(-9)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*-1}=\frac{-18}{-2}
=+9
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*-1}=\frac{-2}{-2}
=1
$