(2x-2)(x-6)=(x+3)(x-2)

Solution for (2x-2)(x-6)=(x+3)(x-2) equation:

(2x-2)(x-6)=(x+3)(x-2)

We move all terms to the left:

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

We multiply parentheses ..

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


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

(x+3)(x-2)

We multiply parentheses ..

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

We get rid of parentheses

x^2-2x+3x-6

We add all the numbers together, and all the variables

x^2+x-6

Back to the equation:

-(x^2+x-6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-15x+18=0

a = 1; b = -15; c = +18;
Δ = b2-4ac
Δ = -152-4·1·18
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{17}}{2*1}=\frac{15-3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{17}}{2*1}=\frac{15+3\sqrt{17}}{2}
$