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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -((x+3)x), so:

(x+3)x

We multiply parentheses

x^2+3x

Back to the equation:

-(x^2+3x)


We get rid of parentheses

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