F(x)=x+3x2-2x-3

Solution for F(x)=x+3x2-2x-3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-3)·3
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{10}}{2*-3}=\frac{-2-2\sqrt{10}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{10}}{2*-3}=\frac{-2+2\sqrt{10}}{-6}
$