F(x)=-(x-20)(x-100)

Solution for F(x)=-(x-20)(x-100) equation:

(F)=-(F-20)(F-100)

We move all terms to the left:

(F)-(-(F-20)(F-100))=0

We multiply parentheses ..

-(-(+F^2-100F-20F+2000))+F=0


We calculate terms in parentheses: -(-(+F^2-100F-20F+2000)), so:

-(+F^2-100F-20F+2000)

We get rid of parentheses

-F^2+100F+20F-2000

We add all the numbers together, and all the variables

-1F^2+120F-2000

Back to the equation:

-(-1F^2+120F-2000)


We get rid of parentheses

1F^2-120F+F+2000=0

We add all the numbers together, and all the variables

F^2-119F+2000=0

a = 1; b = -119; c = +2000;
Δ = b2-4ac
Δ = -1192-4·1·2000
Δ = 6161
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{-(-119)-\sqrt{6161}}{2*1}=\frac{119-\sqrt{6161}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{6161}}{2*1}=\frac{119+\sqrt{6161}}{2}
$