X(2x-3)=54

Solution for X(2x-3)=54 equation:

X(2X-3)=54

We move all terms to the left:

X(2X-3)-(54)=0

We multiply parentheses

2X^2-3X-54=0

a = 2; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·2·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*2}=\frac{-18}{4}
=-4+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*2}=\frac{24}{4}
=6
$