(x-2)(x-1)=4

Solution for (x-2)(x-1)=4 equation:

(x-2)(x-1)=4

We move all terms to the left:

(x-2)(x-1)-(4)=0

We multiply parentheses ..

(+x^2-1x-2x+2)-4=0

We get rid of parentheses

x^2-1x-2x+2-4=0

We add all the numbers together, and all the variables

x^2-3x-2=0

a = 1; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·1·(-2)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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