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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·(-3)·(-2)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*-3}=\frac{6-2\sqrt{3}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*-3}=\frac{6+2\sqrt{3}}{-6}
$