F(-1)=x^2-7x+1

Solution for F(-1)=x^2-7x+1 equation:

(-1)=F^2-7F+1

We move all terms to the left:

(-1)-(F^2-7F+1)=0

We add all the numbers together, and all the variables

-(F^2-7F+1)-1=0

We get rid of parentheses

-F^2+7F-1-1=0

We add all the numbers together, and all the variables

-1F^2+7F-2=0

a = -1; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-1)·(-2)
Δ = 41
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{-(7)-\sqrt{41}}{2*-1}=\frac{-7-\sqrt{41}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*-1}=\frac{-7+\sqrt{41}}{-2}
$