F(-x)=5-6x-5x^2

Solution for F(-x)=5-6x-5x^2 equation:

(-F)=5-6F-5F^2

We move all terms to the left:

(-F)-(5-6F-5F^2)=0

We add all the numbers together, and all the variables

-(5-6F-5F^2)+(-1F)=0

We get rid of parentheses

5F^2+6F-1F-5=0

We add all the numbers together, and all the variables

5F^2+5F-5=0

a = 5; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·5·(-5)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{5}}{2*5}=\frac{-5-5\sqrt{5}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{5}}{2*5}=\frac{-5+5\sqrt{5}}{10}
$