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

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

(F)=4F-3F^2

We move all terms to the left:

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

We get rid of parentheses

3F^2-4F+F=0

We add all the numbers together, and all the variables

3F^2-3F=0

a = 3; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·3·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*3}=\frac{6}{6}
=1
$