x^2-6x=82

Solution for x^2-6x=82 equation:

x^2-6x=82

We move all terms to the left:

x^2-6x-(82)=0

a = 1; b = -6; c = -82;
Δ = b2-4ac
Δ = -62-4·1·(-82)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{91}}{2*1}=\frac{6-2\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{91}}{2*1}=\frac{6+2\sqrt{91}}{2}
$