F(-x)=4x2+5x-1

Solution for F(-x)=4x2+5x-1 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4F^2-6F+1=0

a = -4; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-4)·1
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-4}=\frac{6-2\sqrt{13}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-4}=\frac{6+2\sqrt{13}}{-8}
$