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

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

(F)=-F^2+15F

We move all terms to the left:

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

We get rid of parentheses

F^2-15F+F=0

We add all the numbers together, and all the variables

F^2-14F=0

a = 1; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·1·0
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*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*1}=\frac{28}{2}
=14
$