F(x)=3x-15x^2+18x

Solution for F(x)=3x-15x^2+18x equation:

(F)=3F-15F^2+18F

We move all terms to the left:

(F)-(3F-15F^2+18F)=0

We get rid of parentheses

15F^2-3F-18F+F=0

We add all the numbers together, and all the variables

15F^2-20F=0

a = 15; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·15·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*15}=\frac{0}{30}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*15}=\frac{40}{30}
=1+1/3
$