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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x+2-x(x-6)

determiningTheFunctionDomain
x-x(x-6)+2

We multiply parentheses

-x^2+x+6x+2

We add all the numbers together, and all the variables

-1x^2+7x+2

Back to the equation:

-(-1x^2+7x+2)


We add all the numbers together, and all the variables

-(-1x^2+7x+2)-1x=0

We get rid of parentheses

1x^2-7x-1x-2=0

We add all the numbers together, and all the variables

x^2-8x-2=0

a = 1; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·1·(-2)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*1}=\frac{8-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*1}=\frac{8+6\sqrt{2}}{2}
$