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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2-18x-(x(x+2))=0


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

x(x+2)

We multiply parentheses

x^2+2x

Back to the equation:

-(x^2+2x)


We get rid of parentheses

3x^2-x^2-18x-2x=0

We add all the numbers together, and all the variables

2x^2-20x=0

a = 2; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·2·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*2}=\frac{40}{4}
=10
$