(3x-3)x=(x+6)(2x)

Solution for (3x-3)x=(x+6)(2x) equation:

(3x-3)x=(x+6)(2x)

We move all terms to the left:

(3x-3)x-((x+6)(2x))=0

We multiply parentheses

3x^2-3x-((x+6)2x)=0


We calculate terms in parentheses: -((x+6)2x), so:

(x+6)2x

We multiply parentheses

2x^2+12x

Back to the equation:

-(2x^2+12x)


We get rid of parentheses

3x^2-2x^2-3x-12x=0

We add all the numbers together, and all the variables

x^2-15x=0

a = 1; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·1·0
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{-(-15)-15}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*1}=\frac{30}{2}
=15
$