9+3x=6x(3-x)

Solution for 9+3x=6x(3-x) equation:

9+3x=6x(3-x)

We move all terms to the left:

9+3x-(6x(3-x))=0

We add all the numbers together, and all the variables

3x-(6x(-1x+3))+9=0


We calculate terms in parentheses: -(6x(-1x+3)), so:

6x(-1x+3)

We multiply parentheses

-6x^2+18x

Back to the equation:

-(-6x^2+18x)


We get rid of parentheses

6x^2-18x+3x+9=0

We add all the numbers together, and all the variables

6x^2-15x+9=0

a = 6; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·6·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*6}=\frac{18}{12}
=1+1/2
$