(x-2)x=60

Solution for (x-2)x=60 equation:

(x-2)x=60

We move all terms to the left:

(x-2)x-(60)=0

We multiply parentheses

x^2-2x-60=0

a = 1; b = -2; c = -60;
Δ = b2-4ac
Δ = -22-4·1·(-60)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*1}=\frac{2-2\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*1}=\frac{2+2\sqrt{61}}{2}
$