X(2x-3)=72

Solution for X(2x-3)=72 equation:

X(2X-3)=72

We move all terms to the left:

X(2X-3)-(72)=0

We multiply parentheses

2X^2-3X-72=0

a = 2; b = -3; c = -72;
Δ = b2-4ac
Δ = -32-4·2·(-72)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{65}}{2*2}=\frac{3-3\sqrt{65}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{65}}{2*2}=\frac{3+3\sqrt{65}}{4}
$