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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(3(x-1)), so:

3(x-1)

We multiply parentheses

3x-3

Back to the equation:

-(3x-3)


We multiply parentheses

2x^2-6x-4x-(3x-3)+12=0

We get rid of parentheses

2x^2-6x-4x-3x+3+12=0

We add all the numbers together, and all the variables

2x^2-13x+15=0

a = 2; b = -13; c = +15;
Δ = b2-4ac
Δ = -132-4·2·15
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*2}=\frac{20}{4}
=5
$