X(2x-9)=18

Solution for X(2x-9)=18 equation:

X(2X-9)=18

We move all terms to the left:

X(2X-9)-(18)=0

We multiply parentheses

2X^2-9X-18=0

a = 2; b = -9; c = -18;
Δ = b2-4ac
Δ = -92-4·2·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*2}=\frac{-6}{4}
=-1+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*2}=\frac{24}{4}
=6
$