F(x)=-x2+12x-20

Solution for F(x)=-x2+12x-20 equation:

(F)=-F2+12F-20

We move all terms to the left:

(F)-(-F2+12F-20)=0

We add all the numbers together, and all the variables

-(-1F^2+12F-20)+F=0

We get rid of parentheses

1F^2-12F+F+20=0

We add all the numbers together, and all the variables

F^2-11F+20=0

a = 1; b = -11; c = +20;
Δ = b2-4ac
Δ = -112-4·1·20
Δ = 41
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{41}}{2*1}=\frac{11-\sqrt{41}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{41}}{2*1}=\frac{11+\sqrt{41}}{2}
$