F(x+4)=x^2+7x-9

Solution for F(x+4)=x^2+7x-9 equation:

(F+4)=F^2+7F-9

We move all terms to the left:

(F+4)-(F^2+7F-9)=0

We get rid of parentheses

-F^2+F-7F+4+9=0

We add all the numbers together, and all the variables

-1F^2-6F+13=0

a = -1; b = -6; c = +13;
Δ = b2-4ac
Δ = -62-4·(-1)·13
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{22}}{2*-1}=\frac{6-2\sqrt{22}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{22}}{2*-1}=\frac{6+2\sqrt{22}}{-2}
$