F(x)=3+6x-7x^2

Solution for F(x)=3+6x-7x^2 equation:

(F)=3+6F-7F^2

We move all terms to the left:

(F)-(3+6F-7F^2)=0

We get rid of parentheses

7F^2-6F+F-3=0

We add all the numbers together, and all the variables

7F^2-5F-3=0

a = 7; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·7·(-3)
Δ = 109
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{-(-5)-\sqrt{109}}{2*7}=\frac{5-\sqrt{109}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*7}=\frac{5+\sqrt{109}}{14}
$