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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-((2x-1)(x-3))-6=0

We multiply parentheses ..

-((+2x^2-6x-1x+3))+2x-6=0


We calculate terms in parentheses: -((+2x^2-6x-1x+3)), so:

(+2x^2-6x-1x+3)

We get rid of parentheses

2x^2-6x-1x+3

We add all the numbers together, and all the variables

2x^2-7x+3

Back to the equation:

-(2x^2-7x+3)


We add all the numbers together, and all the variables

2x-(2x^2-7x+3)-6=0

We get rid of parentheses

-2x^2+2x+7x-3-6=0

We add all the numbers together, and all the variables

-2x^2+9x-9=0

a = -2; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·(-2)·(-9)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-2}=\frac{-6}{-4}
=1+1/2
$