F(x)=(10-x)(x-50)

Solution for F(x)=(10-x)(x-50) equation:

(F)=(10-F)(F-50)

We move all terms to the left:

(F)-((10-F)(F-50))=0

We add all the numbers together, and all the variables

F-((-1F+10)(F-50))=0

We multiply parentheses ..

-((-1F^2+50F+10F-500))+F=0


We calculate terms in parentheses: -((-1F^2+50F+10F-500)), so:

(-1F^2+50F+10F-500)

We get rid of parentheses

-1F^2+50F+10F-500

We add all the numbers together, and all the variables

-1F^2+60F-500

Back to the equation:

-(-1F^2+60F-500)


We get rid of parentheses

1F^2-60F+F+500=0

We add all the numbers together, and all the variables

F^2-59F+500=0

a = 1; b = -59; c = +500;
Δ = b2-4ac
Δ = -592-4·1·500
Δ = 1481
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{-(-59)-\sqrt{1481}}{2*1}=\frac{59-\sqrt{1481}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{1481}}{2*1}=\frac{59+\sqrt{1481}}{2}
$