F(-x)=x^2+5x-8

Solution for F(-x)=x^2+5x-8 equation:

(-F)=F^2+5F-8

We move all terms to the left:

(-F)-(F^2+5F-8)=0

We add all the numbers together, and all the variables

(-1F)-(F^2+5F-8)=0

We get rid of parentheses

-F^2-1F-5F+8=0

We add all the numbers together, and all the variables

-1F^2-6F+8=0

a = -1; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-1)·8
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*-1}=\frac{6-2\sqrt{17}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*-1}=\frac{6+2\sqrt{17}}{-2}
$