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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(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-2=0

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