F(x)=6x^2+24x+2

Solution for F(x)=6x^2+24x+2 equation:

(F)=6F^2+24F+2

We move all terms to the left:

(F)-(6F^2+24F+2)=0

We get rid of parentheses

-6F^2+F-24F-2=0

We add all the numbers together, and all the variables

-6F^2-23F-2=0

a = -6; b = -23; c = -2;
Δ = b2-4ac
Δ = -232-4·(-6)·(-2)
Δ = 481
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{-(-23)-\sqrt{481}}{2*-6}=\frac{23-\sqrt{481}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{481}}{2*-6}=\frac{23+\sqrt{481}}{-12}
$