F(-x)=3x^2-4x-2

Solution for F(-x)=3x^2-4x-2 equation:

(-F)=3F^2-4F-2

We move all terms to the left:

(-F)-(3F^2-4F-2)=0

We add all the numbers together, and all the variables

(-1F)-(3F^2-4F-2)=0

We get rid of parentheses

-3F^2-1F+4F+2=0

We add all the numbers together, and all the variables

-3F^2+3F+2=0

a = -3; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-3)·2
Δ = 33
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{-(3)-\sqrt{33}}{2*-3}=\frac{-3-\sqrt{33}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*-3}=\frac{-3+\sqrt{33}}{-6}
$