F(x)=x^2-9x-8

Solution for F(x)=x^2-9x-8 equation:

(F)=F^2-9F-8

We move all terms to the left:

(F)-(F^2-9F-8)=0

We get rid of parentheses

-F^2+F+9F+8=0

We add all the numbers together, and all the variables

-1F^2+10F+8=0

a = -1; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·(-1)·8
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*-1}=\frac{-10-2\sqrt{33}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*-1}=\frac{-10+2\sqrt{33}}{-2}
$