F(x)=3x(x-8)5

Solution for F(x)=3x(x-8)5 equation:

(F)=3F(F-8)5

We move all terms to the left:

(F)-(3F(F-8)5)=0


We calculate terms in parentheses: -(3F(F-8)5), so:

3F(F-8)5

We multiply parentheses

15F^2-120F

Back to the equation:

-(15F^2-120F)


We get rid of parentheses

-15F^2+F+120F=0

We add all the numbers together, and all the variables

-15F^2+121F=0

a = -15; b = 121; c = 0;
Δ = b2-4ac
Δ = 1212-4·(-15)·0
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-121}{2*-15}=\frac{-242}{-30}
=8+1/15
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+121}{2*-15}=\frac{0}{-30}
=0
$