F(x)=-x(3x-18)

Solution for F(x)=-x(3x-18) equation:

(F)=-F(3F-18)

We move all terms to the left:

(F)-(-F(3F-18))=0


We calculate terms in parentheses: -(-F(3F-18)), so:

-F(3F-18)

We multiply parentheses

-3F^2+18F

Back to the equation:

-(-3F^2+18F)


We get rid of parentheses

3F^2-18F+F=0

We add all the numbers together, and all the variables

3F^2-17F=0

a = 3; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·3·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*3}=\frac{34}{6}
=5+2/3
$