F(x)=15x-5x2

Solution for F(x)=15x-5x2 equation:

(F)=15F-5F^2

We move all terms to the left:

(F)-(15F-5F^2)=0

We get rid of parentheses

5F^2-15F+F=0

We add all the numbers together, and all the variables

5F^2-14F=0

a = 5; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·5·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*5}=\frac{0}{10}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*5}=\frac{28}{10}
=2+4/5
$