F(x)=x(60-2x)

Solution for F(x)=x(60-2x) equation:

(F)=F(60-2F)

We move all terms to the left:

(F)-(F(60-2F))=0

We add all the numbers together, and all the variables

F-(F(-2F+60))=0


We calculate terms in parentheses: -(F(-2F+60)), so:

F(-2F+60)

We multiply parentheses

-2F^2+60F

Back to the equation:

-(-2F^2+60F)


We get rid of parentheses

2F^2-60F+F=0

We add all the numbers together, and all the variables

2F^2-59F=0

a = 2; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·2·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*2}=\frac{118}{4}
=29+1/2
$