x(x-1)-60=60-x

Solution for x(x-1)-60=60-x equation:

x(x-1)-60=60-x

We move all terms to the left:

x(x-1)-60-(60-x)=0

We add all the numbers together, and all the variables

x(x-1)-(-1x+60)-60=0

We multiply parentheses

x^2-1x-(-1x+60)-60=0

We get rid of parentheses

x^2-1x+1x-60-60=0

We add all the numbers together, and all the variables

x^2-120=0

a = 1; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·1·(-120)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*1}=\frac{0-4\sqrt{30}}{2}
=-\frac{4\sqrt{30}}{2}
=-2\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*1}=\frac{0+4\sqrt{30}}{2}
=\frac{4\sqrt{30}}{2}
=2\sqrt{30}
$