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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x+3)-(2x(-1x+6))=0

We multiply parentheses

x^2+3x-(2x(-1x+6))=0


We calculate terms in parentheses: -(2x(-1x+6)), so:

2x(-1x+6)

We multiply parentheses

-2x^2+12x

Back to the equation:

-(-2x^2+12x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-9x=0

a = 3; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·3·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*3}=\frac{18}{6}
=3
$