(X-3)(X.X-2x+6)=x(x.x-5x+9)

Solution for (X-3)(X.X-2x+6)=x(x.x-5x+9) equation:

(X-3)(X.X-2X+6)=X(X.X-5X+9)

We move all terms to the left:

(X-3)(X.X-2X+6)-(X(X.X-5X+9))=0

We add all the numbers together, and all the variables

(X-3)(-2X+X.X+6)-(X(-5X+X.X+9))=0

We multiply parentheses ..

(-2X^2+X^2+6X+6X-3X-18)-(X(-5X+X.X+9))=0


We calculate terms in parentheses: -(X(-5X+X.X+9)), so:

X(-5X+X.X+9)

We multiply parentheses

-5X^2+X^2+9X

We add all the numbers together, and all the variables

-4X^2+9X

Back to the equation:

-(-4X^2+9X)


We get rid of parentheses

-2X^2+X^2+4X^2+6X+6X-3X-9X-18=0

We add all the numbers together, and all the variables

3X^2-18=0

a = 3; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·3·(-18)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*3}=\frac{0-6\sqrt{6}}{6}
=-\frac{6\sqrt{6}}{6}
=-\sqrt{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*3}=\frac{0+6\sqrt{6}}{6}
=\frac{6\sqrt{6}}{6}
=\sqrt{6}
$