220-x^2+5x+60=x

Solution for 220-x^2+5x+60=x equation:

220-x^2+5x+60=x

We move all terms to the left:

220-x^2+5x+60-(x)=0

We add all the numbers together, and all the variables

-1x^2+4x+280=0

a = -1; b = 4; c = +280;
Δ = b2-4ac
Δ = 42-4·(-1)·280
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{71}}{2*-1}=\frac{-4-4\sqrt{71}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{71}}{2*-1}=\frac{-4+4\sqrt{71}}{-2}
$