F(x)=x^2-18+6

Solution for F(x)=x^2-18+6 equation:

(F)=F^2-18+6

We move all terms to the left:

(F)-(F^2-18+6)=0

We get rid of parentheses

-F^2+F+18-6=0

We add all the numbers together, and all the variables

-1F^2+F+12=0

a = -1; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-1)·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-1}=\frac{-8}{-2}
=+4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-1}=\frac{6}{-2}
=-3
$