F(-x)=-2x^2+5x-4

Solution for F(-x)=-2x^2+5x-4 equation:

(-F)=-2F^2+5F-4

We move all terms to the left:

(-F)-(-2F^2+5F-4)=0

We add all the numbers together, and all the variables

-(-2F^2+5F-4)+(-1F)=0

We get rid of parentheses

2F^2-5F-1F+4=0

We add all the numbers together, and all the variables

2F^2-6F+4=0

a = 2; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·2·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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