F(x)=x(x+3)2

Solution for F(x)=x(x+3)2 equation:

(F)=F(F+3)2

We move all terms to the left:

(F)-(F(F+3)2)=0


We calculate terms in parentheses: -(F(F+3)2), so:

F(F+3)2

We multiply parentheses

2F^2+6F

Back to the equation:

-(2F^2+6F)


We get rid of parentheses

-2F^2+F-6F=0

We add all the numbers together, and all the variables

-2F^2-5F=0

a = -2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-2}=\frac{0}{-4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-2}=\frac{10}{-4}
=-2+1/2
$