F(X-3)=x^2-5x-8

Solution for F(X-3)=x^2-5x-8 equation:

(F-3)=F^2-5F-8

We move all terms to the left:

(F-3)-(F^2-5F-8)=0

We get rid of parentheses

-F^2+F+5F-3+8=0

We add all the numbers together, and all the variables

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

a = -1; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-1)·5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{14}}{2*-1}=\frac{-6-2\sqrt{14}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{14}}{2*-1}=\frac{-6+2\sqrt{14}}{-2}
$