X(x-1)=x+120

Solution for X(x-1)=x+120 equation:

X(X-1)=X+120

We move all terms to the left:

X(X-1)-(X+120)=0

We multiply parentheses

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

We get rid of parentheses

X^2-1X-X-120=0

We add all the numbers together, and all the variables

X^2-2X-120=0

a = 1; b = -2; c = -120;
Δ = b2-4ac
Δ = -22-4·1·(-120)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*1}=\frac{24}{2}
=12
$