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

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

(F)=(F-1)(F+2)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

F^2+2F-1F-2

We add all the numbers together, and all the variables

F^2+F-2

Back to the equation:

-(F^2+F-2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-F^2+F-F+2=0

We add all the numbers together, and all the variables

-1F^2+2=0

a = -1; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-1)·2
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-1}=\frac{0-2\sqrt{2}}{-2}
=-\frac{2\sqrt{2}}{-2}
=-\frac{\sqrt{2}}{-1}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-1}=\frac{0+2\sqrt{2}}{-2}
=\frac{2\sqrt{2}}{-2}
=\frac{\sqrt{2}}{-1}
$