6X(x-2)=x-6

Solution for 6X(x-2)=x-6 equation:

6X(X-2)=X-6

We move all terms to the left:

6X(X-2)-(X-6)=0

We multiply parentheses

6X^2-12X-(X-6)=0

We get rid of parentheses

6X^2-12X-X+6=0

We add all the numbers together, and all the variables

6X^2-13X+6=0

a = 6; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·6·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*6}=\frac{8}{12}
=2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*6}=\frac{18}{12}
=1+1/2
$