x² = -3x + 1

Get 0 on the right:

 x² + 3x - 1 = 0 

Put a 1 coefficient for the x²

1x² + 3x - 1 = 0

Compare that to the general quadratic equation, which is

ax² + bx + c = 0

and you see that a=1, b=3, and c=-1

Substutute into this 

x = 

x = 

Simplify:

x = 

x = 

The ± symbol means that there are two answers, one using the +
and one using the - :

, 

 

That's it.  Be sure to memorize 

ax² + bx + c = 0

and

x = 

Edwin