F(x)=3x^2+24x-144

Solution for F(x)=3x^2+24x-144 equation:

(F)=3F^2+24F-144

We move all terms to the left:

(F)-(3F^2+24F-144)=0

We get rid of parentheses

-3F^2+F-24F+144=0

We add all the numbers together, and all the variables

-3F^2-23F+144=0

a = -3; b = -23; c = +144;
Δ = b2-4ac
Δ = -232-4·(-3)·144
Δ = 2257
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{2257}}{2*-3}=\frac{23-\sqrt{2257}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{2257}}{2*-3}=\frac{23+\sqrt{2257}}{-6}
$