F(x)=x^2-9x+6

Solution for F(x)=x^2-9x+6 equation:

(F)=F^2-9F+6

We move all terms to the left:

(F)-(F^2-9F+6)=0

We get rid of parentheses

-F^2+F+9F-6=0

We add all the numbers together, and all the variables

-1F^2+10F-6=0

a = -1; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·(-1)·(-6)
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{-(10)-2\sqrt{19}}{2*-1}=\frac{-10-2\sqrt{19}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*-1}=\frac{-10+2\sqrt{19}}{-2}
$