F(x)=4x^2-8x-24

Solution for F(x)=4x^2-8x-24 equation:

(F)=4F^2-8F-24

We move all terms to the left:

(F)-(4F^2-8F-24)=0

We get rid of parentheses

-4F^2+F+8F+24=0

We add all the numbers together, and all the variables

-4F^2+9F+24=0

a = -4; b = 9; c = +24;
Δ = b2-4ac
Δ = 92-4·(-4)·24
Δ = 465
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{-(9)-\sqrt{465}}{2*-4}=\frac{-9-\sqrt{465}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{465}}{2*-4}=\frac{-9+\sqrt{465}}{-8}
$