F(-x)=8x^2+2x-1

Solution for F(-x)=8x^2+2x-1 equation:

(-F)=8F^2+2F-1

We move all terms to the left:

(-F)-(8F^2+2F-1)=0

We add all the numbers together, and all the variables

(-1F)-(8F^2+2F-1)=0

We get rid of parentheses

-8F^2-1F-2F+1=0

We add all the numbers together, and all the variables

-8F^2-3F+1=0

a = -8; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-8)·1
Δ = 41
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{41}}{2*-8}=\frac{3-\sqrt{41}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*-8}=\frac{3+\sqrt{41}}{-16}
$