F(3)=x^2+8x

Solution for F(3)=x^2+8x equation:

(3)=F^2+8F

We move all terms to the left:

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

We get rid of parentheses

-F^2-8F+3=0

We add all the numbers together, and all the variables

-1F^2-8F+3=0

a = -1; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-1)·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{19}}{2*-1}=\frac{8-2\sqrt{19}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{19}}{2*-1}=\frac{8+2\sqrt{19}}{-2}
$