F(x)=-2(x-1)(x-3)

Solution for F(x)=-2(x-1)(x-3) equation:

(F)=-2(F-1)(F-3)

We move all terms to the left:

(F)-(-2(F-1)(F-3))=0

We multiply parentheses ..

-(-2(+F^2-3F-1F+3))+F=0


We calculate terms in parentheses: -(-2(+F^2-3F-1F+3)), so:

-2(+F^2-3F-1F+3)

We multiply parentheses

-2F^2+6F+2F-6

We add all the numbers together, and all the variables

-2F^2+8F-6

Back to the equation:

-(-2F^2+8F-6)


We get rid of parentheses

2F^2-8F+F+6=0

We add all the numbers together, and all the variables

2F^2-7F+6=0

a = 2; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·2·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*2}=\frac{6}{4}
=1+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*2}=\frac{8}{4}
=2
$