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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-1)·3
Δ = 21
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{-(-3)-\sqrt{21}}{2*-1}=\frac{3-\sqrt{21}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*-1}=\frac{3+\sqrt{21}}{-2}
$