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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

(-1x+6)*2x

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
$