3x-3=x(2-x)

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

3x-3=x(2-x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

x(-1x+2)

We multiply parentheses

-1x^2+2x

Back to the equation:

-(-1x^2+2x)


We get rid of parentheses

1x^2-2x+3x-3=0

We add all the numbers together, and all the variables

x^2+x-3=0

a = 1; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·1·(-3)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{13}}{2*1}=\frac{-1-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*1}=\frac{-1+\sqrt{13}}{2}
$