X(2x-6)=154*2

Solution for X(2x-6)=154*2 equation:

X(2X-6)=154*2

We move all terms to the left:

X(2X-6)-(154*2)=0

We add all the numbers together, and all the variables

X(2X-6)-308=0

We multiply parentheses

2X^2-6X-308=0

a = 2; b = -6; c = -308;
Δ = b2-4ac
Δ = -62-4·2·(-308)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-50}{2*2}=\frac{-44}{4}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+50}{2*2}=\frac{56}{4}
=14
$