(x-2)(x-1)=120

Solution for (x-2)(x-1)=120 equation:

(x-2)(x-1)=120

We move all terms to the left:

(x-2)(x-1)-(120)=0

We multiply parentheses ..

(+x^2-1x-2x+2)-120=0

We get rid of parentheses

x^2-1x-2x+2-120=0

We add all the numbers together, and all the variables

x^2-3x-118=0

a = 1; b = -3; c = -118;
Δ = b2-4ac
Δ = -32-4·1·(-118)
Δ = 481
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{481}}{2*1}=\frac{3-\sqrt{481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{481}}{2*1}=\frac{3+\sqrt{481}}{2}
$