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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-4)·2
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*-4}=\frac{4-4\sqrt{3}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*-4}=\frac{4+4\sqrt{3}}{-8}
$