x^2-12x=81

Solution for x^2-12x=81 equation:

x^2-12x=81

We move all terms to the left:

x^2-12x-(81)=0

a = 1; b = -12; c = -81;
Δ = b2-4ac
Δ = -122-4·1·(-81)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{13}}{2*1}=\frac{12-6\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{13}}{2*1}=\frac{12+6\sqrt{13}}{2}
$