X*(2x-6)=108

Solution for X*(2x-6)=108 equation:

X(2X-6)=108

We move all terms to the left:

X(2X-6)-(108)=0

We multiply parentheses

2X^2-6X-108=0

a = 2; b = -6; c = -108;
Δ = b2-4ac
Δ = -62-4·2·(-108)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*2}=\frac{-24}{4}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*2}=\frac{36}{4}
=9
$