F(x)=x(10-3x)

Solution for F(x)=x(10-3x) equation:

(F)=F(10-3F)

We move all terms to the left:

(F)-(F(10-3F))=0

We add all the numbers together, and all the variables

F-(F(-3F+10))=0


We calculate terms in parentheses: -(F(-3F+10)), so:

F(-3F+10)

We multiply parentheses

-3F^2+10F

Back to the equation:

-(-3F^2+10F)


We get rid of parentheses

3F^2-10F+F=0

We add all the numbers together, and all the variables

3F^2-9F=0

a = 3; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·3·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*3}=\frac{18}{6}
=3
$