2x(x-3)=12x

Solution for 2x(x-3)=12x equation:

2x(x-3)=12x

We move all terms to the left:

2x(x-3)-(12x)=0

We add all the numbers together, and all the variables

-12x+2x(x-3)=0

We multiply parentheses

2x^2-12x-6x=0

We add all the numbers together, and all the variables

2x^2-18x=0

a = 2; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·2·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*2}=\frac{36}{4}
=9
$