F(3)=x2+-3x-1

Solution for F(3)=x2+-3x-1 equation:

(3)=F2+-3F-1

We move all terms to the left:

(3)-(F2+-3F-1)=0

We add all the numbers together, and all the variables

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

We use the square of the difference formula

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+3F+4=0

a = -1; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-1}=\frac{-8}{-2}
=+4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-1}=\frac{2}{-2}
=-1
$