(x-1)(x-2)/x-3=0

Solution for (x-1)(x-2)/x-3=0 equation:

(x-1)(x-2)/x-3=0


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

(+x^2-2x-1x+2)/x-3=0

We multiply all the terms by the denominator


(+x^2-2x-1x+2)-3*x=0

We add all the numbers together, and all the variables

(+x^2-2x-1x+2)-3x=0

We get rid of parentheses

x^2-2x-1x-3x+2=0

We add all the numbers together, and all the variables

x^2-6x+2=0

a = 1; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·1·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*1}=\frac{6-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*1}=\frac{6+2\sqrt{7}}{2}
$