6x=x^2-2

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

6x=x^2-2

We move all terms to the left:

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

We get rid of parentheses

-x^2+6x+2=0

We add all the numbers together, and all the variables

-1x^2+6x+2=0

a = -1; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-1)·2
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*-1}=\frac{-6-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*-1}=\frac{-6+2\sqrt{11}}{-2}
$