F(x)=3x^2+15x+6

Solution for F(x)=3x^2+15x+6 equation:

(F)=3F^2+15F+6

We move all terms to the left:

(F)-(3F^2+15F+6)=0

We get rid of parentheses

-3F^2+F-15F-6=0

We add all the numbers together, and all the variables

-3F^2-14F-6=0

a = -3; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·(-3)·(-6)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{31}}{2*-3}=\frac{14-2\sqrt{31}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{31}}{2*-3}=\frac{14+2\sqrt{31}}{-6}
$