F(-x)=x^2+7x+6

Solution for F(-x)=x^2+7x+6 equation:

(-F)=F^2+7F+6

We move all terms to the left:

(-F)-(F^2+7F+6)=0

We add all the numbers together, and all the variables

(-1F)-(F^2+7F+6)=0

We get rid of parentheses

-F^2-1F-7F-6=0

We add all the numbers together, and all the variables

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

a = -1; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·(-1)·(-6)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*-1}=\frac{8-2\sqrt{10}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*-1}=\frac{8+2\sqrt{10}}{-2}
$