F(x)=7x-3x^2

Solution for F(x)=7x-3x^2 equation:

(F)=7F-3F^2

We move all terms to the left:

(F)-(7F-3F^2)=0

We get rid of parentheses

3F^2-7F+F=0

We add all the numbers together, and all the variables

3F^2-6F=0

a = 3; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*3}=\frac{12}{6}
=2
$