F(x)=5x(2-3x)

Solution for F(x)=5x(2-3x) equation:

(F)=5F(2-3F)

We move all terms to the left:

(F)-(5F(2-3F))=0

We add all the numbers together, and all the variables

F-(5F(-3F+2))=0


We calculate terms in parentheses: -(5F(-3F+2)), so:

5F(-3F+2)

We multiply parentheses

-15F^2+10F

Back to the equation:

-(-15F^2+10F)


We get rid of parentheses

15F^2-10F+F=0

We add all the numbers together, and all the variables

15F^2-9F=0

a = 15; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·15·0
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*15}=\frac{0}{30}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*15}=\frac{18}{30}
=3/5
$