F(1)=7x-3x^2

Solution for F(1)=7x-3x^2 equation:

(1)=7F-3F^2

We move all terms to the left:

(1)-(7F-3F^2)=0

We get rid of parentheses

3F^2-7F+1=0

a = 3; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·3·1
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{37}}{2*3}=\frac{7-\sqrt{37}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{37}}{2*3}=\frac{7+\sqrt{37}}{6}
$