X-3x+3=3x(x-1)+3x-9

Solution for X-3x+3=3x(x-1)+3x-9 equation:

X-3X+3=3X(X-1)+3X-9

We move all terms to the left:

X-3X+3-(3X(X-1)+3X-9)=0

We add all the numbers together, and all the variables

-2X-(3X(X-1)+3X-9)+3=0


We calculate terms in parentheses: -(3X(X-1)+3X-9), so:

3X(X-1)+3X-9

We add all the numbers together, and all the variables

3X+3X(X-1)-9

We multiply parentheses

3X^2+3X-3X-9

We add all the numbers together, and all the variables

3X^2-9

Back to the equation:

-(3X^2-9)


We get rid of parentheses

-3X^2-2X+9+3=0

We add all the numbers together, and all the variables

-3X^2-2X+12=0

a = -3; b = -2; c = +12;
Δ = b2-4ac
Δ = -22-4·(-3)·12
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{37}}{2*-3}=\frac{2-2\sqrt{37}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{37}}{2*-3}=\frac{2+2\sqrt{37}}{-6}
$