x^2-6x=260

Solution for x^2-6x=260 equation:

x^2-6x=260

We move all terms to the left:

x^2-6x-(260)=0

a = 1; b = -6; c = -260;
Δ = b2-4ac
Δ = -62-4·1·(-260)
Δ = 1076
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:

$\sqrt{\Delta}=\sqrt{1076}=\sqrt{4*269}=\sqrt{4}*\sqrt{269}=2\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{269}}{2*1}=\frac{6-2\sqrt{269}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{269}}{2*1}=\frac{6+2\sqrt{269}}{2}
$