X(x-6)=9-6x

Solution for X(x-6)=9-6x equation:

X(X-6)=9-6X

We move all terms to the left:

X(X-6)-(9-6X)=0

We add all the numbers together, and all the variables

X(X-6)-(-6X+9)=0

We multiply parentheses

X^2-6X-(-6X+9)=0

We get rid of parentheses

X^2-6X+6X-9=0

We add all the numbers together, and all the variables

X^2-9=0

a = 1; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·1·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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