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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-6x-1=0

a = 1; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·1·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{10}}{2*1}=\frac{6-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{10}}{2*1}=\frac{6+2\sqrt{10}}{2}
$