F(x)=12x^2+24x

Solution for F(x)=12x^2+24x equation:

(F)=12F^2+24F

We move all terms to the left:

(F)-(12F^2+24F)=0

We get rid of parentheses

-12F^2+F-24F=0

We add all the numbers together, and all the variables

-12F^2-23F=0

a = -12; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-12)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-12}=\frac{0}{-24}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-12}=\frac{46}{-24}
=-1+11/12
$