X(3x-24)=65

Solution for X(3x-24)=65 equation:

X(3X-24)=65

We move all terms to the left:

X(3X-24)-(65)=0

We multiply parentheses

3X^2-24X-65=0

a = 3; b = -24; c = -65;
Δ = b2-4ac
Δ = -242-4·3·(-65)
Δ = 1356
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:

$\sqrt{\Delta}=\sqrt{1356}=\sqrt{4*339}=\sqrt{4}*\sqrt{339}=2\sqrt{339}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{339}}{2*3}=\frac{24-2\sqrt{339}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{339}}{2*3}=\frac{24+2\sqrt{339}}{6}
$