F(x+6)=x^2-1

Solution for F(x+6)=x^2-1 equation:

(F+6)=F^2-1

We move all terms to the left:

(F+6)-(F^2-1)=0

We get rid of parentheses

-F^2+F+6+1=0

We add all the numbers together, and all the variables

-1F^2+F+7=0

a = -1; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-1)·7
Δ = 29
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{-(1)-\sqrt{29}}{2*-1}=\frac{-1-\sqrt{29}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{29}}{2*-1}=\frac{-1+\sqrt{29}}{-2}
$