X(2x-8)=24

Solution for X(2x-8)=24 equation:

X(2X-8)=24

We move all terms to the left:

X(2X-8)-(24)=0

We multiply parentheses

2X^2-8X-24=0

a = 2; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·2·(-24)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*2}=\frac{-8}{4}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*2}=\frac{24}{4}
=6
$