F(x)=x^2-10x-2

Solution for F(x)=x^2-10x-2 equation:

(F)=F^2-10F-2

We move all terms to the left:

(F)-(F^2-10F-2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+11F+2=0

a = -1; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·(-1)·2
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{129}}{2*-1}=\frac{-11-\sqrt{129}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{129}}{2*-1}=\frac{-11+\sqrt{129}}{-2}
$