F(x)=240x-16x2

Solution for F(x)=240x-16x2 equation:

(F)=240F-16F^2

We move all terms to the left:

(F)-(240F-16F^2)=0

We get rid of parentheses

16F^2-240F+F=0

We add all the numbers together, and all the variables

16F^2-239F=0

a = 16; b = -239; c = 0;
Δ = b2-4ac
Δ = -2392-4·16·0
Δ = 57121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57121}=239$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-239)-239}{2*16}=\frac{0}{32}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-239)+239}{2*16}=\frac{478}{32}
=14+15/16
$