X^2-6x=81

Solution for X^2-6x=81 equation:

X^2-6X=81

We move all terms to the left:

X^2-6X-(81)=0

a = 1; b = -6; c = -81;
Δ = b2-4ac
Δ = -62-4·1·(-81)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{10}}{2*1}=\frac{6-6\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{10}}{2*1}=\frac{6+6\sqrt{10}}{2}
$