F(2x)=x2+6x-12

Solution for F(2x)=x2+6x-12 equation:

(2F)=F2+6F-12

We move all terms to the left:

(2F)-(F2+6F-12)=0

We add all the numbers together, and all the variables

-(+F^2+6F-12)+2F=0

We get rid of parentheses

-F^2-6F+2F+12=0

We add all the numbers together, and all the variables

-1F^2-4F+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$