F(x)=4x-3x^2+5x

Solution for F(x)=4x-3x^2+5x equation:

(F)=4F-3F^2+5F

We move all terms to the left:

(F)-(4F-3F^2+5F)=0

We get rid of parentheses

3F^2-4F-5F+F=0

We add all the numbers together, and all the variables

3F^2-8F=0

a = 3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·3·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*3}=\frac{16}{6}
=2+2/3
$