81-x^2=2x

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

81-x^2=2x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2-2x+81=0

a = -1; b = -2; c = +81;
Δ = b2-4ac
Δ = -22-4·(-1)·81
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{82}}{2*-1}=\frac{2-2\sqrt{82}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{82}}{2*-1}=\frac{2+2\sqrt{82}}{-2}
$