F(x-2)=x^2+-12

Solution for F(x-2)=x^2+-12 equation:

(F-2)=F^2+-12

We move all terms to the left:

(F-2)-(F^2+-12)=0

We use the square of the difference formula

(F-2)-(F^2-12)=0

We get rid of parentheses

-F^2+F-2+12=0

We add all the numbers together, and all the variables

-1F^2+F+10=0

a = -1; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-1)·10
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{-(1)-\sqrt{41}}{2*-1}=\frac{-1-\sqrt{41}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*-1}=\frac{-1+\sqrt{41}}{-2}
$