X(x-8)=24

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

X(X-8)=24

We move all terms to the left:

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

We multiply parentheses

X^2-8X-24=0

a = 1; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·1·(-24)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*1}=\frac{8-4\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*1}=\frac{8+4\sqrt{10}}{2}
$