0=x^2-x-120

Solution for 0=x^2-x-120 equation:

0=x^2-x-120

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+x+120=0

We add all the numbers together, and all the variables

-1x^2+x+120=0

a = -1; b = 1; c = +120;
Δ = b2-4ac
Δ = 12-4·(-1)·120
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{-(1)-\sqrt{481}}{2*-1}=\frac{-1-\sqrt{481}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{481}}{2*-1}=\frac{-1+\sqrt{481}}{-2}
$