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

Solution for (x^2)-6x=x^-2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

x^2-6x-x^+2=0

We add all the numbers together, and all the variables

x^2-7x+2=0

a = 1; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·1·2
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{41}}{2*1}=\frac{7-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{41}}{2*1}=\frac{7+\sqrt{41}}{2}
$